An audio engineer wishes to obtain a phase lag of between the supply voltage and…

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

Problem

An audio engineer wishes to obtain a phase lag of

75^{\circ}

between the supply voltage and current at a fixed frequency of

5.0\,\text{kHz}

using a series

RLC

network. She can use a resistor of

40\,\Omega

and an inductor of

15\,\text{mH}

. The amplitude of the source voltage is

10\,\text{V}_{\text{rms}}

. (i) Show that the requirement of a

75^{\circ}

lag leads to a quadratic equation in the unknown capacitance

C

. Write this equation explicitly in standard quadratic form. (ii) Solve the equation obtained in part (i) and choose the physically acceptable value of

C

(in

\mu\text{F}

). State clearly the reason for rejecting any inadmissible root. (iii) Using the selected value of

C

, calculate the rms current delivered by the source at

5.0\,\text{kHz}

. (iv) Comment briefly on whether the chosen component values are practical for use in typical audio–frequency circuitry.

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