# How do you find the Total Current in an RC circuit with multiple parallel capacitors and resistors?

I’m an Electro-mechanical engineering student and I have this homework problem from our textbook. It lays out the circuit attached and asked to find the current through each capacitor and resistor and to find the total current. I know how to find total current when there’s just one capacitor and resistor in the circuit but the book didn’t give any examples with multiple capacitors and resistors, so I had to improvise to find the solution. The answer I came up with (191 mA) matches the one the book gives but I want to ask the community if this is the right method or if there’s a better way to find total current in these kinds of circuits. I’ve attached a screenshot with the circuit and my work.

Thanks!

• Each part is in parallel to a source. So if you find the current in each one and then just add them up, you will get the right answer. I get 191.319171 mA and the angle is 65.0154948. Which is what you get. Your resistor values are fine. For C1 I find 0.118123884 j and for C2 I find 0.0552920307 j. With the resistors this adds up to: 0.0808080808 + 0.173415914 j. Commented Apr 21 at 14:28
• The RMS equation you used, squaring the real part and squaring the imaginary part, and taking the root, is good for the magnitude. Same with your method for the angle. You are fine. Commented Apr 21 at 14:34

I know how to find total current $$\\color{red}{\text{when there’s just one capacitor and resistor}}\$$ in the circuit but the book didn’t give any examples with multiple capacitors and resistors, so I had to improvise to find the solution.
$$R_{PARALLEL} = \dfrac{R_1\cdot R_2}{R_1+R_2}$$
For parallel capacitors it's even easier: $$\C_1+C_2\$$.