An $80 Ω$ resistor and $20 μ F$ capacitor are connected in series with AC source $220 V$ and $50 H z$ . Calculate the P.D. across each of them.

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Solution

The reactance is given as,

$X_{C} = \frac{1}{2 π f C}$

$X_{C} = \frac{1}{2 π \times 50 \times 20 \times 10^{- 6}}$

$X_{C} = 159.15 Ω$

The impedance is given as,

$Z = \sqrt{R^{2} + {X_{C}}^{2}}$

$Z = \sqrt{{(80)}^{2} + {(159.15)}^{2}}$

$Z = 178.13 Ω$

The current in the circuit is given as,

$I = \frac{V}{Z}$

$I = \frac{220}{178.13}$

$I = 1.235 A$

The potential drop across the resistance is given as,

$V_{R} = I R$

$V_{R} = 1.235 \times 80$

$V_{R} = 98.8 Ω$

The potential drop across the capacitor is given as,

$V_{C} = I X_{C}$

$V_{C} = 1.235 \times 159.15$

$V_{C} = 196.56 Ω$

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An 80Ω resistor and 20μF capacitor are connected in series with AC source 220V and 50Hz . Calculate the P.D. across each of them.

An $80 Ω$ resistor and $20 μ F$ capacitor are connected in series with AC source $220 V$ and $50 H z$ . Calculate the P.D. across each of them.