Two resistors with resistances R_1 and R_2 ar | vedclass

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Question

(D) In the steady state,the capacitors act as open circuits,so no current flows through the capacitor branch. The potential at point $a$ relative to t

Vedclass · Accepted Answer

$R_1 C_1 = R_2 C_2$

Vedclass · Answer

(D) In the steady state,the capacitors act as open circuits,so no current flows through the capacitor branch. The potential at point $a$ relative to the negative terminal of the battery is determined by the voltage divider rule for resistors: $V_a = \frac{\varepsilon R_2}{R_1 + R_2}$.Similarly,the potential at point $b$ relative to the negative terminal is determined by the voltage divider rule for capacitors: $V_b = \frac{\varepsilon C_1}{C_1 + C_2}$.For the potential difference between $a$ and $b$ to be zero,we must have $V_a = V_b$.Therefore,$\frac{\varepsilon R_2}{R_1 + R_2} = \frac{\varepsilon C_1}{C_1 + C_2}$.Simplifying this,$R_2(C_1 + C_2) = C_1(R_1 + R_2)$.$R_2 C_1 + R_2 C_2 = C_1 R_1 + C_1 R_2$.$R_2 C_2 = R_1 C_1$.

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