Difficulty: Easy
Correct Answer: Both A and R are true and R is the correct explanation of A
Explanation:
Introduction / Context:Hot-wire ammeters are based on the heating effect of current. Their scale is not uniform but cramped at lower values due to the square-law relationship between current and heating. Understanding the assertion and reasoning requires connecting the thermal principle with scale graduation.
Given Data / Assumptions:
Concept / Approach:If heat ∝ I^2, then deflection θ ∝ I^2. Thus, small increases in current cause disproportionately small increases in deflection at the lower end, resulting in cramped spacing of scale divisions.
Step-by-Step Solution:
Step 1: Heat H = I^2 × R × t.Step 2: Deflection θ ∝ H.Step 3: Hence θ ∝ I^2.Step 4: The quadratic nature produces cramped (non-linear) scale at the start.Verification / Alternative check:
Experimental hot-wire ammeter curves show scale compressions at low readings.Why Other Options Are Wrong:
Since both A and R are true and linked directly, other combinations are invalid.Common Pitfalls:
Confusing linear instruments (PMMC) with thermal instruments; forgetting quadratic law.Final Answer:
Both A and R are true and R is the correct explanation of A
Discussion & Comments