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A $100 \Omega$ resistor is connected to a $220 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
Solution:
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Verified Answer
Given: Resistance $R=100 \Omega$
Voltage $\mathrm{E}_{\mathrm{v}}=220 \mathrm{~V}$
frequency $v=50 \mathrm{~Hz}$
To find: (a) rms current (b) net power.
Formula: (a) $I_v=\frac{E_v}{R}$ (b) $P=I_v{ }^2 R$
(a) $\mathrm{I}_{\mathrm{v}}=\frac{\mathrm{E}_{\mathrm{v}}}{\mathrm{R}}=\frac{220}{100}=2.2 \mathrm{~A}$
(b) $\mathrm{P}_{\mathrm{ay}}=\mathrm{I}_{\mathrm{y}}^2 \mathrm{R}=(2.2)^2 \times 100=484 \mathrm{~W}$
Voltage $\mathrm{E}_{\mathrm{v}}=220 \mathrm{~V}$
frequency $v=50 \mathrm{~Hz}$
To find: (a) rms current (b) net power.
Formula: (a) $I_v=\frac{E_v}{R}$ (b) $P=I_v{ }^2 R$
(a) $\mathrm{I}_{\mathrm{v}}=\frac{\mathrm{E}_{\mathrm{v}}}{\mathrm{R}}=\frac{220}{100}=2.2 \mathrm{~A}$
(b) $\mathrm{P}_{\mathrm{ay}}=\mathrm{I}_{\mathrm{y}}^2 \mathrm{R}=(2.2)^2 \times 100=484 \mathrm{~W}$
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