The switch S illustrated in the figure is kept closed for a long duration and is subsequently opened at t = 0 . Determine the current in the middle 10 resistor at t = 1.0 ms .

Step-by-step solution

When the switch S is closed for a long time, the circuit reaches a steady state. In this state, the capacitor acts as an open circuit and no current flows through its branch. The steady current I flows through the outer loop containing the 12 V battery and the two 10 resistors in series: I = 12 10 + 10 = 0.6 A The potential difference across the middle 10 resistor is: V₀ = I 10 = 0.6 10 = 6 V Since the capacitor is in parallel with this resistor, the initial voltage across the capacitor is V₀ = 6 V . When the switc