An RC circuit with a 1-Ω resistor and a 0.000001-F capacitor is driven by a voltage E(t)=sin(100t)V. If the initial capacitor voltage is zero, determine the subsequent resistor and capacitor voltages and the current.
So far I have found the capacitor voltage but am stuck on the resistor and current, can someone point me in the right direction please?
We want to write a differential equation to represent this circuit. The voltage around the circuit must sum to 0, so we can write the differential equation by finding the changes in voltage at each part and writing an equation in which they sum to 0.
You already have the voltage for the battery: $E(t) = sin(100t)$.
The voltage of a resistor can be found using the equation $V = IR$. Since the resistance is $1 \Omega$, we can substitute that in for $R$ and write $V = I$.
The voltage of a capacitor can be found using the equation $Q = CV$, which we can rearrange as $V = Q/C$. Since the capacitance is $10^{-6}$, we can substitute this in for $C$ and write $V = 10^6Q$.
Use these terms to write a single differential equation and then solve.
That should be enough to get you going! Hope it helps!