First slide

AC Circuits

Question

The angular frequency of alternating current in a L.C.R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Difficult

A

$0.8 H a n d 250 μ F$
B

$1.33 H a n d 250 μ F$
C

$1.33 H a n d 150 μ F$
D

$0.8 H a n d 150 μ F$

Solution

Since, key is open R' will not participate in circuit.
$\begin{array}{l} 15 = i_{r m s} (60) (v = i R) \\ \Rightarrow i_{r m s} = \frac{15}{60} \\ \Rightarrow i_{r m s} = \frac{1}{4} A \\ Now, 20 = \frac{1}{4} (X_{L}) [v = i X_{L}] \\ \Rightarrow 20 = \frac{1}{4} (ω L) \\ \Rightarrow 20 = \frac{1}{4} (100 L) \\ \Rightarrow L = \frac{20}{25} \\ \Rightarrow L = \frac{4}{5} \\ \Rightarrow L = 0.8 H \\ And 10 = \frac{1}{4} (X_{C}) [v = i X_{C}] \\ \Rightarrow 10 = \frac{1}{4} (\frac{1}{ω C}) \\ \Rightarrow 10 = \frac{1}{4} (\frac{1}{100 C}) \\ \Rightarrow C = \frac{1}{4 \times 10^{3}} \\ \Rightarrow C = 0.25 \times 10^{- 3} F \\ \Rightarrow C = 250 \times 10^{- 6} F \\ \Rightarrow C = 250 μ F \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App