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AC Applied to a Resistor

Two series re...

Question

Two series resistors are connected to an ac source. If there are $7.5 V$ rms across one resistor and $4.2 V$ rms across the other, the peak source voltage is

A

16.54 V

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B

1.65 V

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C

10.60 V

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D

5.93 V

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Solution

The correct option is A $16.54 V$
Total rms voltage of the source $V_{r m s} = V_{{r m s}_{1}} + V_{{r m s}_{2}}$
$∴$ $V_{r m s} = 7.5 V + 4.2$ $V$
$⟹$ $V_{r m s} = 11.7 V$
Thus peak voltage $V_{o} = \sqrt{2} V_{r m s}$
$⟹$ $V_{o} = 1.414 \times 11.7 = 16.54 V$

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