In the following circuit R_1=3 Ohm, R_2=10 Ohm, C=0.003 Farad, V=5 Volts.

At time t =0 we connect the power supply to the circuit. At t=0 the capacitor is uncharged.

(a) What is the time constant tau (in seconds) to charge up the capacitor?

(b) What is the electric potential over the capacitor when it is fully charged?

(c) Calculate the current delivered by the power supply as a function of time and evaluate it (in Ampere) for t=0.6 tau, where tau is the value obtained in part (a).

(d) What is the current delivered by the power supply when the capacitor is fully charged?

(e) How much energy (in Joules) is in the capacitor when it is fully charged?

please do help on this one

To answer the questions, we need to use the formulas related to charging and discharging of an RC circuit.

(a) The time constant (tau) of the RC circuit is given by the product of the resistance (R) and the capacitance (C), i.e., tau = R * C. In this case, tau = 3 Ohm * 0.003 Farad = 0.009 seconds.

(b) When the capacitor is fully charged, it reaches the same potential as the power supply. Therefore, the electric potential across the capacitor when it is fully charged is equal to the voltage of the power supply, which is V = 5 Volts.

(c) To calculate the current as a function of time, we can use the equation: I(t) = (V/R) * (1 - e^(-t/tau)), where I(t) is the current at time t, V is the voltage, R is the resistance, and tau is the time constant. Plugging in the values, we have I(t) = (5 V / 3 Ohm) * (1 - e^(-t/(0.009 seconds))). To evaluate it for t = 0.6 tau, we substitute t = 0.6 * 0.009 seconds into the equation and calculate the result.

(d) When the capacitor is fully charged, no current flows through it. Therefore, the current delivered by the power supply when the capacitor is fully charged is zero Ampere.

(e) The energy stored in a capacitor is given by the formula: E = (1/2) * C * V^2, where E is the energy, C is the capacitance, and V is the voltage across the capacitor. Plugging in the values, we have E = (1/2) * 0.003 Farad * (5 Volts)^2. Calculate this to find the energy in Joules when the capacitor is fully charged.