A ballistic galvanometer shows a first swing of 25° when a charge of 100 μC passes through it. What charge is required for a first swing of 50° (assume proportionality of first swing to total charge)?
Electronics and Communication Engineering
Measurements and Instrumentation
Difficulty: Easy
Choose an option
-
A200 μC
-
B400 μC
-
C50 μC
-
D25 μC
-
E100 μC
Answer
Correct Answer: 200 μC
Explanation
Introduction / Context:A ballistic galvanometer is designed to measure total charge passed in a short pulse. Its initial deflection (first swing) is proportional to the impulse of current and hence to the total charge, provided damping is small and the pulse duration is short compared with the galvanometer period. This is a standard proportional-scaling question.
Given Data / Assumptions:
- First swing θ ∝ Q (total charge).
- Case 1: Q1 = 100 μC → θ1 = 25°.
- Case 2: Q2 → θ2 = 50°.
- Same instrument settings and conditions; damping unchanged.
Concept / Approach:Since θ ∝ Q, the ratio of deflections equals the ratio of charges. Doubling the first swing from 25° to 50° requires doubling the charge through the galvanometer.
Step-by-Step Solution:
θ2 / θ1 = Q2 / Q1.50 / 25 = Q2 / 100 ⇒ Q2 = 200 μC.Verification / Alternative check:
Linear proportionality is a core assumption in ballistic mode for small angles; experimental plots confirm near-proportional behavior around this range.Why Other Options Are Wrong:
400 μC would quadruple the swing; 50 μC or 25 μC would reduce it; 100 μC would keep it at 25°.Common Pitfalls:
Confusing steady-state galvanometers (deflection ∝ current) with ballistic operation (deflection ∝ charge).Final Answer:
200 μC