A current of 2.45 A flows through a 39 microFarads capacitor connected across a 50 Hz supply. Detérmine the supply voltage. (3 marks)June/July 2020

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To determine the supply voltage in this problem, we can use the formula for the voltage across a capacitor in an a.c circuit:

V = IXC

where V is the voltage across the capacitor, I is the current through the capacitor, and XC is the reactance of the capacitor.

The reactance of a capacitor is given by the formula:

XC = 1/(2πfC)

where f is the frequency of the a.c supply (in Hz) and C is the capacitance of the capacitor (in Farads).

In this case, we are given that the current through the capacitor is 2.45 A, the capacitance of the capacitor is 39 microFarads (which is equivalent to 0.000039 Farads), and the frequency of the a.c supply is 50 Hz.

Substituting these values into the formula for the reactance of a capacitor, we get:

XC = 1/(2π(50 Hz)(0.000039 Farads)) = 31.83 ohms

Substituting the values for I, XC, and C into the formula for the voltage across a capacitor in an a.c circuit, we get:

V = (2.45 A)(31.83 ohms) = 78.5 V

Therefore, the supply voltage in this case is 78.5 V