Problem 93 - A Complete Resource Book in Physics for JEE Main

Question

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) \(2 \Omega\)

Step-by-Step Solution

Answer

The value of the shunt resistor needed to convert the given galvanometer into an ammeter with a full-scale current reading of 20 A is 0.5 Ω, which corresponds to option (A).

Step 1: Galvanometer current and resistance

Given that the galvanometer has a resistance of 19.5 Ω and gives full-scale deflection for a current of 0.5 A. So, Resistance of galvanometer (G) = 19.5 Ω Current passing through galvanometer (Ig) = 0.5 A Step 2: Setting up the total current for the ammeter we desire

Step 2: Total ammeter current

It is desired to convert the given galvanometer into an ammeter with a full-scale current reading of 20 A. Let's denote this desired current as Id. Desired ammeter current (Id) = 20 A Step 3: Calculating the current through the shunt resistor

Step 3: Current through shunt resistor

By applying Kirchhoff's Current Law, the sum of the currents through the galvanometer and shunt resistor is equal to the total current through the desired ammeter (20 A). So, the current through the shunt resistor (Is) = Id - Ig = 20 A - 0.5 A = 19.5 A Step 4: Calculating the value of the shunt resistor

Step 4: Value of the shunt resistor

As we know, Ohm's law states that V = IR, where V is voltage, I is current, and R is resistance. Also, the voltage across the shunt resistor (Vs) and the galvanometer (Vg) will be the same. Now, we can write the equation, Vg = Vs, or Ig * G = Is * S, where S is the resistance of the shunt resistor. We need to find the value of S. Rearranging the equation, we have S = (Ig * G) / Is. Substituting the values, we have: S = (0.5 A * 19.5 Ω) / 19.5 A = 0.5 Ω So, the value of the shunt resistor is 0.5 Ω, which corresponds to option (A).