A resistor with resistance (R) is connected in parallel with an inductor with an inductance (L). The net impedance of the circuit is given by
A)
$$R + j \omega L$$ ,
B) $$R - j \omega L$$
C) $$\frac { 1 } { \frac { 1 } { R } + \frac { 1 } { j \omega L } }$$
D) $$\frac { 1 } { \frac { 1 } { R } - \frac { 1 } { j \omega L } }$$

Question

A resistor with resistance (R) is connected in parallel with an inductor with an inductance (L). The net impedance of the circuit is given by
A) 
 $$R + j \omega L$$ ,
B) $$R - j \omega L$$
C) $$\frac { 1 } { \frac { 1 } { R } + \frac { 1 } { j \omega L } }$$
D) $$\frac { 1 } { \frac { 1 } { R } - \frac { 1 } { j \omega L } }$$

Quizplus · Accepted Answer

When a resistor and an inductor are connected in parallel, the total impedance of the circuit is given by
$$Z_{total} = \frac{1}{\frac{1}{R}+\frac{1}{j\omega L}}$$
Simplifying the above equation, we get
$$Z_{total} = \frac{j\omega L R}{j\omega L +R}$$
Therefore, the net impedance of the circuit is C) $$\frac { 1 } { \frac { 1 } { R } + \frac { 1 } { j \omega L } }$$

A Resistor with Resistance (R) Is Connected in Parallel with an Inductor