Chapter 14

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be (Assuming potential difference is same in both cases). (A) One-fourth (B) Halved (C) Doubled (D) Four times

There are \(n\) similar resistors each of resistance \(R\). The equivalent resistance comes out to be \(x\) when connected in parallel. If they are connected in series, the resistance comes out to be (A) \(x / n^{2}\) (B) \(n^{2} x\) (C) \(x / n\) (D) \(n x\)

A cell of emf \(E\) is connected across a resistance \(R\). The potential difference between the terminals of the cell is found to be \(V\). The internal resistance of the cell must be (A) \(\frac{2(E-V) V}{R}\) (B) \(\frac{2(E-V) R}{E}\) (C) \(\frac{(E-V) R}{V}\) (D) \((E-V) R\)

The resistances \(500 \Omega\) and \(1000 \Omega\) are connected in series with a battery of \(1.5 \mathrm{~V}\). The voltage across the \(1000 \Omega\) resistance is measured by a voltmeter having a resistance of \(1000 \Omega\). The reading in the voltmeter would be (A) \(1.5 \mathrm{~V}\) (B) \(1.0 \mathrm{~V}\) (C) \(0.75 \mathrm{~V}\) (D) \(0.5 \mathrm{~V}\)

A set of \(n\) identical resistors, each of resistance \(R \Omega\), when connected in series, has an effective resistance of \(x\) ohm. When the resistors are connected in parallel, the effective resistance is \(y\) ohm. What is the relation between \(R, x\), and \(y ?\) (A) \(R=\frac{x y}{(x+y)}\) (B) \(R=(y-x)\) (C) \(R=\sqrt{x y}\) (D) \(R=(x+y)\)

Five cells, each of EMF \(E\) and internal resistance \(r\) are connected in series. If due to oversight, one cell is connected wrongly, then the equivalent EMF and internal resistance of the combination, is (A) \(5 E\) and \(5 r\) (B) \(3 E\) and \(3 r\) (C) \(3 E\) and \(5 r\) (D) \(5 E\) and \(3 r\)

A wire with resistance \(12 \Omega\) is bent in the form of a circle. The effective resistance between the two points on any diameter of the circle is (A) \(12 \Omega\) (B) \(24 \Omega\) (C) \(6 \Omega\) (D) \(3 \Omega\)

When cells are connected in series (A) the EMF increases. (B) the potential difference decreases. (C) the current capacity increases. (D) the current capacity decreases.

Which of the following has the maximum resistance? (A) Voltmeter (B) Millivoltmeter (C) Ammeter (D) Milliammeter

A wire \(l=8 \mathrm{~m}\) long of uniform cross-sectional area \(A=8 \mathrm{~mm}^{2}\) has a conductance of \(G=2.45 \Omega^{-1}\). The resistivity of material of the wire will be (A) \(2.1 \times 10^{-7} \Omega \mathrm{m}\) (B) \(3.1 \times 10^{-7} \Omega \mathrm{m}\) (C) \(4.1 \times 10^{-7} \Omega \mathrm{m}\) (D) \(5.1 \times 10^{-7} \Omega \mathrm{m}\)

A galvanometer of resistance \(400 \Omega\) can measure a current of \(1 \mathrm{~mA}\). To convert it into a voltmeter of range \(8 \mathrm{~V}\), the required resistance is (A) \(4600 \Omega\) (B) \(5600 \Omega\) (C) \(6600 \Omega\) (D) \(7600 \Omega\)

An ammeter reads up to \(1 \mathrm{~A}\). Its internal resistance is \(0.81 \Omega\). To increase the range to \(10 \mathrm{~A}\), the value of the required shunt is (A) \(0.03 \Omega\) (B) \(0.3 \Omega\) (C) \(0.9 \Omega\) (D) \(0.09 \Omega\)

The resistance of the series combination of two resistances is \(S\). When they are joined in parallel, the total resistance is \(P\). If \(S=n P\), then the minimum possible value of \(n\) is (A) 4 (B) 3 (C) 2 (D) 1

A wire of resistance \(4 \Omega\) is stretched to twice its original length. What is the resistance of the wire now? (A) \(1 \Omega\) (B) \(14 \Omega\) (C) \(8 \Omega\) (D) \(16 \Omega\)

Kirchhoff's second law is based on the law of conservation of (A) Momentum (B) Charge (C) Energy (D) Sum of mass and energy

What is the current through the resistor \(R\) in the circuit shown below? The EMF of each cell is \(E_{m}\) and internal resistance is \(r\) (A) \(\frac{E_{m}}{2 R+r}\) (B) \(\frac{E_{m}}{2 r+R}\) (C) \(\frac{2 E_{m}}{R+2 r}\) (D) \(\frac{2 E_{m}}{2 R+r}\)

The current at which a fuse wire melts does not depend on its (A) Cross-sectional area (B) Length (C) Resistivity (D) Density

In the circuit shown in Fig. \(14.27\), the heat produced in the \(5 \Omega\) resistor due to a current flowing in it is 10 calories per second. The heat produced in the \(4 \Omega\) resistor is (A) \(1 \mathrm{cal} \mathrm{s}^{-1}\) (B) \(2 \mathrm{cal} \mathrm{s}^{-1}\) (C) \(3 \mathrm{cal} \mathrm{s}^{-1}\) (D) \(4 \mathrm{cal} \mathrm{s}^{-1}\)

\(n\) identical cells, each of emf \(\varepsilon\) and internal resistance \(r\), are joined in series to form a closed circuit. The potential difference across any one cell is (A) Zero (B) \(\varepsilon\) (C) \(\frac{\varepsilon}{n}\) (D) \(\frac{n-1}{n} \varepsilon\)

If \(\mathrm{EMF}\) in a thermocouple is \(\varepsilon=\alpha T+\beta T^{2}\), then the neutral temperature of the thermocouple is (A) \(-\beta /(2 \alpha)\) (B) \(-2 \beta / \alpha\) (C) \(-\alpha /(2 \beta)\) (D) \(-2 \alpha / \beta\)

The charge flowing through a resistance \(R\) varies with time \(t\) as \(Q=a t-b t^{2} .\) The total heat produced in \(R\) from \(t=0\) to the time when value of \(Q\) becomes again zero is (A) \(\frac{a^{3} R}{6 b}\) (B) \(\frac{a^{3} R}{3 b}\) (C) \(\frac{a^{3} R}{2 b}\) (D) \(\frac{a^{3} R}{b}\)

The charge flowing through a resistance \(R\) varies with time \(t\) as \(Q=a t-b t^{2} .\) The total heat produced in \(R\) from \(t=0\) to the time when value of \(Q\) becomes again zero is (A) \(\frac{a^{3} R}{6 b}\) (B) \(\frac{a^{3} R}{3 b}\) (C) \(\frac{a^{3} R}{2 b}\) (D) \(\frac{a^{3} R}{b}\)

In the given circuit, find the equivalent resistance between points \(A\) and \(B\). (A) \(18 \Omega\) (B) \(12 \Omega\) (C) \(20 \Omega\) (D) \(27 \Omega\)

The resistance of a wire is \(10 \Omega\). Its length is increased by \(10 \%\) by stretching. The new resistance will now be nearly (A) \(12 \Omega\) (B) \(1.2 \Omega\) (C) \(13 \Omega\) (D) \(11 \Omega\)

The same mass of copper is drawn into two wires \(1 \mathrm{~mm}\) and \(2 \mathrm{~mm}\) thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio (A) \(2: 1\) (B) \(1: 16\) (C) \(4: 1\) (D) \(16: 1\)

\(A B\) is a wire of uniform resistance. The galvanometer \(G\) shows zero current when the length \(A C=20 \mathrm{~cm}\) and \(C B=80 \mathrm{~cm}\). The resistance \(R\) is equal to (A) \(2 \Omega\) (B) \(8 \Omega\) (C) \(20 \Omega\) (D) \(40 \Omega\)

Two cells with the same EMF \(E\) and different internal resistances \(r_{1}\) and \(r_{2}\) are connected in series to an external resistance \(R\). The value of \(R\) for the potential difference across the first cell to be zero is (A) \(\sqrt{r_{1} r_{2}}\) (B) \(r_{1}+r_{2}\) (C) \(r_{1}-r_{2}\) (D) \(\frac{r_{1}+r_{2}}{2}\)

\(A, B\), and \(C\) are voltmeters of resistances \(R, 1.5 R\), and \(3 R\), respectively. When some potential difference is applied between \(X\) and \(Y\), the voltmeter readings are \(V_{A}, V_{B}\), and \(V_{C}\), respectively. (A) \(V_{A}=V_{B}=V_{C}\) (B) \(V_{A} \neq V_{B}=V_{C}\) (C) \(V_{A}=V_{B} \neq V_{C}\) (D) \(V_{B} \neq V_{A}=V_{C}\)

A galvanometer of resistance \(19.5 \Omega\) gives full-scale deflection when a current of \(0.5 \mathrm{~A}\) is passed through it. It is desired to convert it into an ammeter of full-scale current \(20 \mathrm{~A}\). Value of shunt is (A) \(0.5 \Omega\) (B) \(1 \Omega\) (C) \(1.5 \Omega\) (D) \(2 \Omega\)

In the arrangement shown, the magnitude of each resistance is \(2 \Omega\). The equivalent resistance between \(O\) and \(A\) is given by (A) \(\frac{14}{15} \Omega\) (B) \(\frac{7}{15} \Omega\) (C) \(\frac{4}{3} \Omega\) (D) \(\frac{5}{6} \Omega\)

In the circuit shown, if point \(O\) is earthed, the potential of point \(X\) is equal to (A) \(10 \mathrm{~V}\) (B) \(15 \mathrm{~V}\) (C) \(25 \mathrm{~V}\) (D) \(12.5 \mathrm{~V}\)

An ammeter is obtained by shunting a \(30 \Omega\) galvanometer with a \(30 \Omega\) resistance. What additional shunt should be connected across it to double the range? (A) \(15 \Omega\) (B) \(10 \Omega\) (C) \(5 \Omega\) (D) None of these

A voltmeter and an ammeter are connected in series to an ideal cell of EMF \(E\). The voltmeter reading is \(V\), and the ammeter reading is \(I .\) (A) \(V

A dielectric slab of thickness \(d\) is inserted in a parallel plate capacitor whose negative plate is at \(x=0\) and positive plate is at \(x=3 d\). The slab is equidistant from the plates. The capacitor is given some charge. As \(x\) goes from 0 to \(3 d\), (A) the magnitude of the electric field remains the same. (B) the direction of the electric field remains the same. (C) the electric potential increases continuously. (D) the electric potential increases at first, then decreases and again increases.

Two heaters designed for the same voltage \(V\) have different power ratings. When connected individually across a source of voltage \(V\), they produce \(H\) amount of heat each in time \(t_{1}\) and \(t_{2}\), respectively. When used together across the same source, they produce \(H\) amount of heat in time \(t\), (A) if they are in series, \(t=t_{1}+t_{2}\). (B) if they are in series, \(t=2\left(t_{1}+t_{2}\right)\). (C) if they are in parallel, \(t=2\left(t_{1}-t_{2}\right)\). (D) if they are in parallel, \(t=\frac{t_{1} t_{2}}{2\left(t_{1}+t_{2}\right)}\).

A positively charged conducting ball \(B\) is placed inside a cavity of a positively charged conductor \(A \cdot A\) and \(B\) are isolated from each other. If the charges on \(A\) and \(B\) be \(Q\) and \(q(Q>q)\), respectively, then (A) the charge on the outer surface of conductor \(A\) is \(Q+q\) (B) potential of \(B\) is greater than potential of \(A\). (C) when \(B\) touches the surface of \(A\), then potential of \(A\) and \(B\) become same. (D) no charge is left on \(B\) when it touches the surface of \(A\)

The average bulk resistivity of the human body (apart from the surface resistance of the skin) is about \(5 \Omega m\). The conducting path between the hands can be represented approximately as a cylinder \(1.6 \mathrm{~m}\) long and \(0.1 \mathrm{~m}\) diameter. The skin resistance may be made negligible by soaking the hands in salt water. A lethal shock current needed is \(100 \mathrm{~mA}\). Note that a small amount of potential difference could be fatal if the skin is damp. What is the resistance between the hands? (A) \(10^{2} \Omega\) (B) \(10^{3} \Omega\) (C) \(10^{4} \Omega\) (D) None of these

The average bulk resistivity of the human body (apart from the surface resistance of the skin) is about \(5 \Omega m\). The conducting path between the hands can be represented approximately as a cylinder \(1.6 \mathrm{~m}\) long and \(0.1 \mathrm{~m}\) diameter. The skin resistance may be made negligible by soaking the hands in salt water. A lethal shock current needed is \(100 \mathrm{~mA}\). Note that a small amount of potential difference could be fatal if the skin is damp. What potential difference is needed between the hands for a lethal shock current? (A) \(100 \mathrm{~V}\) (B) \(10 \mathrm{~V}\) (C) \(120 \mathrm{~V}\) (D) \(150 \mathrm{~V}\)

The average bulk resistivity of the human body (apart from the surface resistance of the skin) is about \(5 \Omega m\). The conducting path between the hands can be represented approximately as a cylinder \(1.6 \mathrm{~m}\) long and \(0.1 \mathrm{~m}\) diameter. The skin resistance may be made negligible by soaking the hands in salt water. A lethal shock current needed is \(100 \mathrm{~mA}\). Note that a small amount of potential difference could be fatal if the skin is damp. The power dissipated in the body is (A) \(1 \mathrm{~W}\) (B) \(0.1 \mathrm{~W}\) (C) \(100 \mathrm{~W}\) (D) \(10 \mathrm{~W}\)

A potentiometer is a device used for measuring EMF and internal resistance of a cell. It consists of two circuits, one is main circuit in which there is a cell of given emf \(\varepsilon^{\prime}\) and given resistance \(R\) which is connected across a wire of length \(100 \mathrm{~cm}\) and having resistance \(r\) and another circuit having unknown EMF \(\varepsilon\) and galvanometer. For a given potentiometer, if \(\varepsilon^{\prime}=30 \mathrm{~V}, r=1 \Omega\), and resistance \(R\) varies with time \(t\) given by \(R=2 t\). The jockey can move on wire with constant velocity \(10 \mathrm{~cm} / \mathrm{s}\) and switch \(S\) is closed at \(t=0\)If jockey starts moving from \(A\) at \(t=0\) and balancing point found at \(t=1 \mathrm{~s}\) then the value of \(\varepsilon\) is (A) \(1 \mathrm{~V}\) (B) \(2 \mathrm{~V}\) (C) \(3 \mathrm{C}\) (D) \(4 \mathrm{~V}\)

A potentiometer is a device used for measuring EMF and internal resistance of a cell. It consists of two circuits, one is main circuit in which there is a cell of given emf \(\varepsilon^{\prime}\) and given resistance \(R\) which is connected across a wire of length \(100 \mathrm{~cm}\) and having resistance \(r\) and another circuit having unknown EMF \(\varepsilon\) and galvanometer. For a given potentiometer, if \(\varepsilon^{\prime}=30 \mathrm{~V}, r=1 \Omega\), and resistance \(R\) varies with time \(t\) given by \(R=2 t\). The jockey can move on wire with constant velocity \(10 \mathrm{~cm} / \mathrm{s}\) and switch \(S\) is closed at \(t=0\) If balancing length is found to be \(70 \mathrm{~cm}\), then the time after which jockey starts moving from \(A\) is (A) \(1 \mathrm{~s}\) (B) \(2 \mathrm{~s}\) (C) \(3 \mathrm{~s}\) (D) \(4 \mathrm{~s}\)

Figure \(14.47\) shows the circuit of a potentiometer. The length of the potentiometer wire \(A B\) is \(50 \mathrm{~cm}\). The EMF \(E_{1}\) of the battery is \(4 \mathrm{~V}\), having negligible internal resistance. Value of \(R_{1}\) and \(R_{2}\) are \(15 \Omega\) and \(5 \Omega\), respectively. When both the keys are open, the null point is obtained at a distance of \(31.25 \mathrm{~cm}\) from \(A\), but when both the keys are closed, the balance length reduces to \(5 \mathrm{~cm}\) only. Given \(R_{A B}=10 \Omega\)The EMF of the cell \(E_{2}\) is (A) \(1 \mathrm{~V}\) (B) \(2 \mathrm{~V}\) (C) \(3 \mathrm{~V}\) (D) \(4 \mathrm{~V}\)

Figure \(14.47\) shows the circuit of a potentiometer. The length of the potentiometer wire \(A B\) is \(50 \mathrm{~cm}\). The EMF \(E_{1}\) of the battery is \(4 \mathrm{~V}\), having negligible internal resistance. Value of \(R_{1}\) and \(R_{2}\) are \(15 \Omega\) and \(5 \Omega\), respectively. When both the keys are open, the null point is obtained at a distance of \(31.25 \mathrm{~cm}\) from \(A\), but when both the keys are closed, the balance length reduces to \(5 \mathrm{~cm}\) only. Given \(R_{A B}=10 \Omega\) The internal resistance of the cell \(E_{2}\) is (A) \(4.5 \Omega\) (B) \(5.5 \Omega\) (C) \(6.5 \Omega\) (D) \(7.5 \Omega\)

Figure \(14.47\) shows the circuit of a potentiometer. The length of the potentiometer wire \(A B\) is \(50 \mathrm{~cm}\). The EMF \(E_{1}\) of the battery is \(4 \mathrm{~V}\), having negligible internal resistance. Value of \(R_{1}\) and \(R_{2}\) are \(15 \Omega\) and \(5 \Omega\), respectively. When both the keys are open, the null point is obtained at a distance of \(31.25 \mathrm{~cm}\) from \(A\), but when both the keys are closed, the balance length reduces to \(5 \mathrm{~cm}\) only. Given \(R_{A B}=10 \Omega\) The balance length when key \(K_{2}\) is open and \(K_{1}\) is closed is given by (A) \(10.5 \mathrm{~cm}\) (B) \(11.5 \mathrm{~cm}\) (C) \(12.5 \mathrm{~cm}\) (D) \(13.5 \mathrm{~cm}\)

Figure \(14.47\) shows the circuit of a potentiometer. The length of the potentiometer wire \(A B\) is \(50 \mathrm{~cm}\). The EMF \(E_{1}\) of the battery is \(4 \mathrm{~V}\), having negligible internal resistance. Value of \(R_{1}\) and \(R_{2}\) are \(15 \Omega\) and \(5 \Omega\), respectively. When both the keys are open, the null point is obtained at a distance of \(31.25 \mathrm{~cm}\) from \(A\), but when both the keys are closed, the balance length reduces to \(5 \mathrm{~cm}\) only. Given \(R_{A B}=10 \Omega\) The balance length when key \(K_{1}\) is open and \(K_{2}\) is closed is given by (A) \(10.5 \mathrm{~cm}\) (B) \(11.5 \mathrm{~cm}\) (C) \(12.5 \mathrm{~cm}\) (D) \(25 \mathrm{~cm}\)

Consider two identical cells each of \(\mathrm{EMF} E\) and internal resistance \(r\) connected to a load resistance \(R\) Column-I Column-II (A) For maximum power 1\. \(\frac{E^{2}}{4 r}\) transferred to load if cells are connected in series (B) For maximum power transferred to load if 2\. \(\frac{E^{2}}{2 r}\) cells are connected in parallel (C) For series combina- 3\. \(E_{\mathrm{eq}}=E, r_{\mathrm{eq}}=\frac{r}{2}\) tion of cells (D) For parallel combina- 4\. \(E_{\mathrm{eq}}=2 E, r_{\mathrm{eq}}=2 r\) tion of cells

Assertion: Three identical very large metallic plates having charges \(Q,-Q\), and \(3 Q\), respectively are placed parallel. If middle is earthed through a switch, then charge flow through the switch is \(-Q\). Reason: In above assertion, final charge on middle plate is \(-4 Q\). (A) A (B) \(\mathrm{B}\) (C) \(\mathrm{C}\) (D) D

A resistance of \(4 \Omega\) and a wire of length \(5 \mathrm{~m}\) and resistance \(5 \Omega\) are joined in series and connected to a cell of EMF \(10 \mathrm{~V}\) and internal resistance \(1 \Omega\). A parallel combination of two identical cells is balanced across \(300 \mathrm{~cm}\) of the wire. The EMF of each cell is

Two conductors have the same resistance at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_{1}\) and \(\alpha_{2} .\) The respective temperature coefficients of their series and parallel combinations are nearly (A) \(\frac{\alpha_{1}+\alpha_{2}}{2}, \alpha_{1}+\alpha_{2}\) (B) \(\alpha_{1}+\alpha_{2}, \frac{\alpha_{1}+\alpha_{2}}{2}\) (C) \(\alpha_{1}+\alpha_{2}, \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}}\) (D) \(\frac{\alpha_{1}+\alpha_{2}}{2}, \frac{\alpha_{1}+\alpha_{2}}{2}\)

The resistance of a wire is \(5 \Omega\) at \(50^{\circ} \mathrm{C}\) and \(6 \Omega\) at \(100^{\circ} \mathrm{C}\). The resistance of the wire at \(0^{\circ} \mathrm{C}\) will be (A) \(2 \Omega\) (B) \(1 \Omega\) (C) \(4 \Omega\) (D) \(3 \Omega\)