Question

A $200\Omega$resistor is connected to an AC source with ${\in }_o=10V$. What is the peak current through the resistor if the emf frequency is (a) $100Hz$? (b) $100kHz$?

Short answer

Result is:

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

Step-by-step solution

Part(a) Step 1: Given information

We have been given that$R=200\Omega$and${\epsilon }_o=10\mathrm{V}$

Part(a) Step 2: Simplify

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

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

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

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

Part(b) Step 1: Given information

We have been given that$R=200\Omega$and${\epsilon }_o=10\mathrm{V}$

Part(b) Step 2: simplify

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

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

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