Two different series circuits, A and B

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

Problem

Two different series

LCR

circuits, A and B, are designed to operate at the same resonant frequency. (i) Derive a general relation connecting

L_A

C_A

and

L_B

C_B

when the resonant frequencies of both circuits are identical. (ii) Circuit A has

L_A = 100\,\text{mH}

and an unknown

C_A

. Circuit B has

L_B = 25\,\text{mH}

and

C_B = 1.0\,\mu\text{F}

. Using the relation obtained in part (i), calculate

C_A

. (iii) Both circuits are connected separately to an AC source of rms voltage

50\,\text{V}

. If the resistances are

R_A = 30\,\Omega

and

R_B = 20\,\Omega

respectively, determine which circuit will draw the larger rms current at resonance and justify your answer quantitatively.