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GUJCET · Physics · Alternating Current
In RC AC circuit maximum voltage and maximum currents are 100 V and 1.1 A respectively. If \(X_{C}=60 \Omega\) and \(R=80\) ohms then power consumed in the circuit will be ____________ .
- A 176.0 W
- B 44.0 W
- C 88.0 W
- D 22.0 W
Answer & Solution
Correct Answer
(B) 44.0 W
Step-by-step Solution
Detailed explanation
(B) 44.0 W
power
\(
\begin{aligned}
\mathrm{P} & =\mathrm{VI} \cos \phi \\
= & \frac{U_{m}}{\sqrt{2}} \times \frac{i_{m}}{\sqrt{2}} \times \frac{\mathrm{R}}{\sqrt{\mathrm{R}^{2}+\mathrm{X}_{\mathrm{C}}^{2}}} \\
\therefore \mathrm{P} & =\frac{100 \times 1.1 \times 80}{2 \times \sqrt{(80)^{2}+(60)^{2}}} \\
\mathrm{P} & =\frac{4400}{100} \\
\mathrm{P} & =44 \mathrm{~W}
\end{aligned}
\)
power
\(
\begin{aligned}
\mathrm{P} & =\mathrm{VI} \cos \phi \\
= & \frac{U_{m}}{\sqrt{2}} \times \frac{i_{m}}{\sqrt{2}} \times \frac{\mathrm{R}}{\sqrt{\mathrm{R}^{2}+\mathrm{X}_{\mathrm{C}}^{2}}} \\
\therefore \mathrm{P} & =\frac{100 \times 1.1 \times 80}{2 \times \sqrt{(80)^{2}+(60)^{2}}} \\
\mathrm{P} & =\frac{4400}{100} \\
\mathrm{P} & =44 \mathrm{~W}
\end{aligned}
\)
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