Question

A 200 Ω resistor is connected to an AC source with ${\epsilon }_0$=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:$I_o$=50mA

Step-by-step solution

Part(a) Step 1 : Given information

$R=200\Omega$

${\epsilon }_o=10\mathrm{V}$

Frequency =100Hz

Part (a) Step 2: Simplify 

Peak current is given by$I=\frac{{\epsilon }_o}{R}$,does not depend upon frequency

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

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

$I_o=0.05\mathrm{A}\Rightarrow 50\mathrm{mA}$

Part(b) Step 1 : Given information

$R=200\Omega$

${\epsilon }_o=10\mathrm{V}$

Frequency=100 kHz

Part (b) Step 2: Simplify 

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

$I_0=\frac{{\epsilon }_o}{R^{}}$

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

$I_o=0.05\mathrm{A}\Rightarrow 50\mathrm{mA}$