A resistor , an inductor and a capacitor are connected in series to an a.c. source…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A resistor

R

, an inductor

L

and a capacitor

C

are connected in series to an a.c. source having rms voltage

V

and angular frequency

\omega

. (i) Draw the phasor diagram showing the individual voltage drops across

R

L

and

C

and the source voltage. (ii) Apply Kirchhoff’s voltage law to obtain the vector equation relating the source voltage and the three individual voltage drops. (iii) From the above relation, derive an expression for the magnitude of the impedance

Z

of the circuit and show that

Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}

Related theory

Kirchhoff's Laws
AC Circuit Analysis
Series LCR circuit
AC applied to a series LCR circuit
Alternating Current

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