The output emf of an ac generator is 10 sin 100πt. The ac generator is connected to the following circuit elements individually:

Question

The output emf of an ac generator is \(10\sin100\pi t.\) The ac generator is connected to the following circuit elements individually: 

a. 100-ohm Resistor b. 10μF Capacitor c. 10mH Inductor.

Determine the instantaneous voltage and current through each one of them

Answer 1

a. 100 ohm Resistor: 

Voltage across R = \(10\sin100\pi t\) 

Current i = V/R 

\(= 10\sin100\pi t /100 \) 

\(= 0.1 \sin100πt\) 

b. 10μF Capacitor: 

Voltage across C = \(10\sin100πt\)

Current i = \(10\sin100πt /X_c\) 

Here X_c = 1/Cω = 1000/π ohm

Current through C = i = V/X_c

\(= 10\sin(100πt + π/2) / (1000/π)\) 

_{\(=\frac{10\sin(100 \pi t + \frac{\pi}{2})}{\frac{1000}{\pi}} = \frac{\pi}{100}\sin(100 \pi t + \frac{\pi}{2})\)} 

c. 10mH Inductor : 

Voltage across L = \(10\sin100πt\)

Inductive reactance, X_L = Lω = 10 x 10^-3 x 100π = π ohm 

Current through an inductor, i = V/X_L 

_{\(= \frac{10}{\pi}\sin(100 \pi t - \frac{\pi}{2})\)}