Q89 / 110 · VITEEE 2023 · Physics
In an A.C. circuit resistance \(R\), inductance \(L\) and capacitance \(C\) are in parallel. The value of \(R\) is \(50 \Omega\), inductive reactance \(\mathrm{X}_{\mathrm{L}}=40 \Omega\) and capacitive reactance \(\mathrm{X}_{\mathrm{C}}=25 \Omega\). Then the reading of ammeter will be:
- A\(10.2 \mathrm{~A}\)
- Correct answerB\(5 \mathrm{~A}\)
- C\(17 \mathrm{~A}\)
- D\(7 \mathrm{~A}\)
Solution
\(\begin{aligned}
& \mathrm{I}=\sqrt{\mathrm{I}^2{ }_{\mathrm{R}}+\left(\mathrm{I}_{\mathrm{C}}-\mathrm{I}_{\mathrm{L}}\right)^2} \\
& \mathrm{I}_{\mathrm{R}}=\frac{\mathrm{E}}{\mathrm{R}}=\frac{200}{50}=4 \mathrm{~A} \\
& \mathrm{I}_{\mathrm{C}}=\frac{\mathrm{E}}{\mathrm{X}_{\mathrm{C}}}=\frac{200}{25}=8 \mathrm{~A} \\
& \mathrm{I}_{\mathrm{L}}=\frac{\mathrm{E}}{\mathrm{X}_{\mathrm{L}}}=\frac{200}{40}=5 \mathrm{~A} \\
& \mathrm{I}=\sqrt{(4)^2+(8-5)^2} \\
& \mathrm{I}=\sqrt{16+9}=\sqrt{25} \\
& \mathrm{I}=5 \mathrm{~A}
\end{aligned}\)
Hence, the correct answer is option: 'B'.