In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to :
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This is an LR circuit. Initially, with C connected to A, current becomes constant at I₀ = V/R. At t=0, C is switched to B, making it a discharging LR circuit. The current decays as I(t) = I₀e^(-t/τ), where τ = L/R.
Voltage across resistor, V_R = I(t)R = RI₀e^(-t/τ).
Voltage across inductor, V_L = -L(dI/dt) = -L(-I₀/τ e^(-t/τ)) = (L/τ)I₀e^(-t/τ). Since τ = L/R, L/τ = R, so V_L = RI₀e^(-t/τ).
At t = L/R = τ, the ratio V_R / V_L = [RI₀e^(-1)] / [RI₀e^(-1)] = 1.
Final Answer: 1