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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.

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:

  • 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
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