In a circuit, L,C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°.The value of C is:
\(\bigg(\frac{(1)}{(2πf(2πfL + R)}\bigg)\)
\(\bigg(\frac{(1)}{(πf(2πfL + R)}\bigg)\)
\(\bigg(\frac{(1)}{(2πf(2πfL - R)}\bigg)\)
\(\bigg(\frac{(1)}{(πf(2πfL - R)}\bigg)\)
The Correct Option is C
Solution and Explanation
tan \(\phi\) = \(\frac{X_C-X_L}{R}\)
The current leads voltage by 450,
∴tan 45=\(\frac{\frac{1}{2πfc} −2πfL}{R}\)
\(\Rightarrow\) C= \(\frac{1}{2πf(2πfL+R)}\)
Therefore, the correct option is (C): \(\frac{1}{2πf(2πfL+R)}\)
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Concepts Used:
LCR Circuit
An LCR circuit, also known as a resonant circuit, or an RLC circuit, is an electrical circuit consist of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel.
Series LCR circuit
When a constant voltage source is connected across a resistor a current is induced in it. This current has a unique direction and flows from the negative to positive terminal. Magnitude of current remains constant.
Alternating current is the current if the direction of current through this resistor changes periodically. An AC generator or AC dynamo can be used as AC voltage source.
