The capacitor in the figure (figure 1) is initially uncharged. the switch is closed at t=0.

immediately after the switch is closed, what is the current through the resistor r1?

immediately after the switch is closed, what is the current through the resistor r2?

immediately after the switch is closed, what is the current through each resistor r3?

what is the final charge on the capacitor?

Immediately after the switch is closed, the capacitor acts like a short circuit for a very small time. We can calculate the currents through each resistor by first calculating the total resistance:

Req = 1/(1/3+1/6) + 8 = 1/(3/6) + 8 = 2 + 8 = 10 ohms.
IR1 = E / Req = 42 / 10 = 4.2 A.
VR2 = VR3 = E * R23 / Req = 42 * 2 / 10 = 8.4 V
IR2 = VR2 / R2 = 8.4 / 6 = 1.4 A.
IR3 = VR3 / R3 = 8.4 / 3 = 2.8 A.

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