Problem 53 - Master Resource Book in JEE Main Physics

Question

The turns ratio of transformer is given as \(2: 3 .\) If the current passing through the primary coil is \(3 \mathrm{~A}\). Find the current through the load resistance. (a) \(4.5 \mathrm{~A}\) (b) \(1.5 \mathrm{~A}\) (c) \(2 \mathrm{~A}\) (d) \(\mid \mathrm{A}\) The \(\bar{n}\) tuxe 4

Step-by-Step Solution

Answer

The current through the load resistance is 4.5 A, option (a).

Step 1: Understanding the Turns Ratio

The turns ratio of a transformer is given as \(2:3\), meaning for every 2 turns on the primary coil, there are 3 turns on the secondary coil. This ratio can be used to determine the relationship between the currents in the primary and secondary coils.

Step 2: Using the Transformer Current Relationship Formula

For transformers, the current and turns relationship is given by the formula \( \frac{I_p}{I_s} = \frac{N_s}{N_p} \), where \(I_p\) is the primary current, \(I_s\) is the secondary current, \(N_p\) is the number of turns on the primary coil, and \(N_s\) is the number of turns on the secondary coil. In this situation, \(N_p = 2\) and \(N_s = 3\).

Step 3: Substituting Known Values

We know the primary current is \(I_p = 3\, \text{A}\), \(N_p = 2\), and \(N_s = 3\). By substituting into the equation, we have: \[ \frac{3}{I_s} = \frac{3}{2} \].

Step 4: Solving for Secondary Current

From the equation \( \frac{3}{I_s} = \frac{3}{2} \), cross-multiply to solve for \(I_s\). This gives: \[ 3 \times 3 = 2 \times I_s \]. Thus, \(9 = 2I_s\) or \[ I_s = \frac{9}{2} = 4.5\, \text{A} \].

Step 5: Selecting the Correct Answer

Compare the calculated secondary current (4.5 A) with the options provided. The correct choice is (a) 4.5 A.

Key Concepts

Primary coil current

Understanding the primary coil current is crucial in solving transformer problems. In transformers, the primary coil is the coil where the electrical current initially enters. This coil is connected to the input power source. When working with transformers, it's important to remember that the current in the primary coil (\(I_p\)) is the current provided by the power source. In this exercise, the primary coil current is given as 3 A. This is the starting point for calculating the secondary coil current. Remember, no matter how much the turns ratio changes or how different the secondary current might be, the primary current is based on the power input to the transformer.

Secondary coil current

The secondary coil current refers to the current flowing through the coil connected to the output, or load, of the transformer. This coil receives the transformed voltage and current due to the induction process from the primary coil.The main factor determining the secondary current (\(I_s\)) is the turns ratio of the transformer. For this example, the turns ratio is 2:3, which means the secondary current can be calculated using the importance of the ratio in the transformer formula. By applying the formula and using the primary current, you can find that in this scenario, the secondary current turns out to be 4.5 A. This current is delivered to whatever load is connected to the transformer's secondary side.

Transformer formulas

Transformer formulas are essential tools for determining relationships between voltages, currents, and turns ratios in transformers. The fundamental equation in this context is \(\frac{I_p}{I_s} = \frac{N_s}{N_p}\). This formula links the currents and the number of turns on the primary (\(N_p\)) and secondary (\(N_s\)) coils, making it possible to calculate unknowns by substitution.For voltage, we often use the equation \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\), which connects primary and secondary voltages similarly to how current is calculated. By understanding and correctly applying these formulas, one can solve transformer-related problems efficiently, determining unknown voltages and currents based on given values and the turns ratio. This understanding allows for the calculation of essential parameters necessary for designing or analyzing electrical systems involving transformers.