NEET Physics Question - Current Electricity

Assertion (A): When a wire is stretched, then its resistance changes directly as square of its length.

Reason (R): When wire is stretched its thickness/ radius decreases and volume remains constant.

(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(3) (A) is true but (R) is false

(4) Both (A) and (R) are false

Solution:

Resistance of a wire is given by \(R = rho L/A\), where \(rho\) is resistivity, \(L\) is length, and \(A\) is cross-sectional area. When a wire is stretched, its volume \(V = AL\) remains constant. So, \(A = V/L\). Substituting this into the resistance formula, we get \(R = rho L / (V/L) = rho L^2 / V\). Since \(rho\) and \(V\) are constant, \(R propto L^2\). Thus, Assertion (A) is true. When stretched, the length increases, and for constant volume, the cross-sectional area (and thus thickness/radius) must decrease. So, Reason (R) is true. Reason (R) correctly explains why \(R propto L^2\).

Rankers Physics

Stretched Wire Resistance

Solution:

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