An alternating emf source with amplitude 14.9 14.9 V and an adjustable driving frequency f d fd is connected in series with a 59.4 59.4 Ω resistor and a 23.7 23.7 μF capacitor. At what value of f d fd are the amplitudes of the voltages across the resistor and capacitor equal?

113.0 Hz

Explanation:

In a RC circuit with alternating current, the voltage across the resistor is given by Ohm's Law:

where

I is the current in the circuit

R is the resistance of the resistor

While the voltage across the capacitor is given by:

where

is the impedance of the capacitor, where

f is the frequency

C is the capacitance

The voltages across the resistor and the capacitor are equal when

So

Which can be rewritten as

In this problem:

is the resistance

is the capacitance

Substituting, we find the frequency at which this happens:

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where are the vectors ?