In an electric circuit, a wire of resistance 10 Ω is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
[amp_mcq option1=”half of its original value.” option2=”double of its original value.” option3=”one-fourth of its original value.” option4=”four times of its original value.” correct=”option3″]
This question was previously asked in
UPSC NDA-1 – 2023
The resistance of a wire depends on its material (resistivity), length, and cross-sectional area. When a wire is stretched, its length increases, and its cross-sectional area decreases, while its volume remains constant. This change in dimensions affects the resistance. The current in the circuit is inversely proportional to the resistance (assuming constant voltage).
– Resistance R = $\rho \frac{L}{A}$, where $\rho$ is resistivity, L is length, and A is cross-sectional area.
– Volume of the wire V = A × L. When stretched, the volume remains constant: $A’L’ = AL$.
– Ohm’s Law: Current I = Voltage V / Resistance R.