An industrial heating element can be modeled as a coil of resistance and inductance

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

Problem

An industrial heating element can be modeled as a coil of resistance

20\,\Omega

and inductance

0.10\,\text{H}

. It is to be operated from a

240\,\text{V}

(rms),

50\,\text{Hz}

mains supply. A capacitor is connected in series with the coil so that the overall power factor becomes

0.90

(lagging). (i) Derive an expression for the power factor of a series

R

–

L

–

C

circuit in terms of

R

L

C

and the angular frequency of the supply. (ii) Using the result of part (i), calculate the capacitance that must be connected in series with the coil to achieve the required power factor. (iii) For the capacitance found in part (ii), determine the rms current drawn from the mains and the average power consumed by the heating element.

Related theory

Power in AC Circuits
AC Circuit Analysis
Series LCR circuit
AC applied to a series LCR circuit
Alternating Current

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