A series RLC circuit is excited by an alternating emf of peak value and angular…

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

A series RLC circuit is excited by an alternating emf of peak value

V_m

and angular frequency

\omega

. (i) Write the expression for the impedance

Z

of the circuit in terms of

R

L

C

and

\omega

. (ii) Using the result of part (i), obtain an expression for the peak current

I_m

as a function of

\omega

. (iii) Show mathematically that the current amplitude attains a maximum at a particular angular frequency

\omega_0

and hence obtain the value of

I_{m,\text{max}}

. (iv) If the resistance of the circuit is doubled while

L

and

C

remain unchanged, explain qualitatively how the maximum current amplitude will be affected and give a reason.