Question

A galvanometer of resistance 520 \(\Omega\) is shunted with 20 \(\Omega\) resistance to convert it into an ammeter. The resistance of the ammeter will be

• A. 16.8 \(\Omega\)
• B. 540 \(\Omega\)
• C. 19.3 \(\Omega\)
• D. 18 \(\Omega\)

Hint:

Remember that the equivalent resistance of a parallel combination is always less than the smallest individual resistance in the combination. Here, the smallest resistance is the shunt (20 \(\Omega\)), so the answer must be less than 20 \(\Omega\). This can help you eliminate incorrect options like 540 \(\Omega\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
To convert a galvanometer into an ammeter, a low-resistance wire called a "shunt" is connected in parallel with the galvanometer. The resulting device, the ammeter, has an overall resistance that is the equivalent resistance of the galvanometer and the shunt connected in parallel. An ideal ammeter should have zero resistance.

Step 2: Key Formula or Approach:
When two resistors, \(R_G\) (galvanometer resistance) and \(R_S\) (shunt resistance), are connected in parallel, their equivalent resistance \(R_A\) (resistance of the ammeter) is given by: \[ \frac{1}{R_A} = \frac{1}{R_G} + \frac{1}{R_S} \] or, more conveniently for two resistors: \[ R_A = \frac{R_G \times R_S}{R_G + R_S} \]

Step 3: Detailed Explanation:
Given data:
Galvanometer resistance, \(R_G = 520 \, \Omega\).
Shunt resistance, \(R_S = 20 \, \Omega\).
Calculation:
Substitute the values into the formula for parallel equivalent resistance: \[ R_A = \frac{520 \times 20}{520 + 20} \] \[ R_A = \frac{10400}{540} \] \[ R_A = \frac{1040}{54} = \frac{520}{27} \] \[ R_A \approx 19.259 \, \Omega \] Rounding to one decimal place, we get 19.3 \(\Omega\).

Step 4: Final Answer:
The resistance of the ammeter will be approximately 19.3 \(\Omega\).