Question

A 200 Ω resistor is connected to an AC source with E0=10 V. What is the peak current through the resistor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

Short answer

Result is:$I_0=50\mathrm{mA}$

Step-by-step solution

Part (a) Step 1 : Given information

R = 200Ω

${\epsilon }_0$=10V

Frequency=100Hz

Part (a) Step 2 : Simplify

Peak Current is given by $I=\frac{{\epsilon }_o}{R^{}}$, does not depend on frequency.

$I_o=\frac{{\epsilon }_o}{R}$

$I_o=\frac{10\mathrm{V}}{200\Omega }$

$I_{\mathit{0}\mathit{=}\mathit{0}\mathit{.}\mathit{05}\mathit{A}}$

$I_{0=50mA}$

Part (b) Step 1 : Given information

R = 200Ω

${\epsilon }_0$=10V

Frequency=100 kHz

Part (b) Step 2 : Simplify

Peak Current is given by $I_o=\frac{{\epsilon }_o}{R}$, does not depend on frequency.

$I_o=\frac{{\epsilon }_o}{R}$

$I_o=\frac{10V}{200\Omega }$

$I_o=0.05\mathrm{A}$

$I_{0=50mA}$