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Question

Why does the power dissipated in a resistor increase quadratically with current?

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Explanation

**Potential difference drop** across resistor when current flows because charges lose potential energy qV = I² R t as heat, field E = V/l drives drift, maintaining current. At very high E, velocity saturation or heating changes τ, causing non-ohmic behaviour. Power P = I² R . Since power depends on the square of the current ( I² ), doubling the current quadruples the power, assuming resistance remains constant. Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields Power depends on current squared,

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