Answer to Question #177217 in Electric Circuits for Ashhab Danhalidu

Question

A 10k resistor , 10mH inductor and 10uF capacitor are connected in series with a 10KHz voltage source . The rms current through the circuit is 0.20A. Find the rms voltage across each of the 3 elements? 

Answer 1

Explanations & Calculations

• Same current pass through each component since they are connected in series.
• Then the potential drop across each is given by

1. For the resistor,

$\qquad\qquad \begin{aligned} \small V_R&=\small IR=0.20A\times10^4\Omega\\ &=\small \bold{2000V} \end{aligned}$

2 , For the inductor,

$\qquad\qquad \begin{aligned} \small |V_L|&=\small I\omega L=2\pi fL\cdot I\\ &=\small 2\pi\times (10^4s^{-1})\times(10\times10^{-3}H)\times0.2A\\ &=\small \bold{125.66V}[\text{leading the current by 90deg.}] \end{aligned}$

3, For the capacitor,

$\qquad\qquad \begin{aligned} \small |V_c|&=\small \frac{I}{\omega C}=\frac{I}{2\pi f C}\\ &=\small \frac{0.2A}{2\pi\times10^4s^{-1}\times10\times10^{-6}F}\\ &=\small \bold{0.318V}[\text{lagging the current by 90 deg.}] \end{aligned}$