Assertion (A): A hot-wire ammeter has a cramped (non-linear) scale. Reason (R): The heat produced in the wire is proportional to the square of the current passing through it.
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ABoth A and R are true and R is the correct explanation of A
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BBoth A and R are true but R is not the correct explanation of A
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CA is true, R is false
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DA is false, R is true
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EBoth A and R are false
Answer
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:
- Heating effect: H ∝ I^2 × R × t.
- Deflection of pointer is proportional to heat produced.
- Scale markings depend on deflection response.
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