An 18 V battery with an internal resistance of 1 is connected to a parallel combination of two branches. The first branch contains a 4 resistor in series with an unknown resistor R . The second branch contains a 1 resistor and a 2 resistor in series. A branch containing a 3 F capacitor in series with a 5 resistor is connected in parallel across the unknown resistor R . If the steady-state charge on the capacitor is 1

Step-by-step solution

In steady state, the capacitor acts as an open circuit, so no current flows through the 5 resistor in series with it. The potential difference across the capacitor is V_C = Q C = 12 C 3 F = 4 V . Since the capacitor branch is connected in parallel across the unknown resistor R and has no current, the voltage across R is also V_R = 4 V . The current in the first branch is I₁ = V_R R = 4 R . The total voltage across the parallel combination is V_p = I₁ (4 + R) = 4 R (4 + R) = 16 R + 4 . The equivalent resistance of t