Question

A 70.0 Hz generator with an rms voltage of 145 V is connected in series to a 3.70 kΩ resistor and a 3.15 μF capacitor.

Part A.) Find the rms current in the circuit. I found part A's answer to be 38.5mA.

I need help on Part B: Find the phase angle, ϕ, between the current and the voltage.

Answer 1

Answer 2

To find the phase angle $\varphi$ between the current and voltage in this series RC circuit:

1. Calculate the capacitive reactance ($X_C$):

   $$X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 70\times 3.15\times 10^{-6}}\approx 721.5\mathrm{\Omega }$$

2. Use the resistor value ($R=3.7\text{k}\mathrm{\Omega }=3700\mathrm{\Omega }$) and $X_C$ to find the phase angle:

   $$\varphi ={\tan }^{-1}\left(\frac{-X_C}{R}\right)={\tan }^{-1}\left(\frac{-721.5}{3700}\right)\approx -11.0^{\circ }$$

The negative sign means the current leads the voltage by $11.0^{\circ }$.

Using a calculator (in degree mode):

$$\varphi \approx -11.0^{\circ }$$

Short answer: The phase angle is approximately 11.0 degrees, with the current ahead of the voltage.

Interpretation:

• The negative angle means the current leads the voltage by $11.0^{\circ }$.

• If we express it as a positive angle in lag terms, it would be $\varphi =349^{\circ }$, but by convention, we report the smallest magnitude, so $-11.0^{\circ }$ is standard.