Problem 1 (15 points): Consider the three resistor-capacitor circuits shown in the gure below. Each of the capacitors has a capacitance of C. Each resistor has a resistance of R. at r\" j} a) Find the equivalent resistance, the equivalent capacitance, and the RC time constant for each circuit (in terms of R and/or C). b) Now consider only circuit 1, replacing the switch with a battery of II emf 8 = 15 V. The resistance of each resistor is R = 609 and the capacitance of each (initially uncharged) capacitor is C = 10oF. I i. What is the current through each resistor immediately after the battery is connected? ii. Once the battery is connected, the current begins to decrease as the capacitors charge. How much time will it take for the Current to decrease to 13.5% of its original value? (Hint: 0.135 is approximately equal to 1/92) iii. What is the current through each resistor after the battery has been connected for a very long time