MHT CET · Physics · Alternating Current
A series \(\mathrm{L}-\mathrm{C}-\mathrm{R}\) circuit containing a resistance of \(120 \Omega\) has angular frequency \(4 \times 10^5 \mathrm{rad} \mathrm{s}^{-1}\). At resonance the voltage across resistance and inductor are \(60 \mathrm{~V}\) and \(40 \mathrm{~V}\) respectively, then the value of inductance will be
- A \(0.2 \mathrm{mH}\)
- B \(0.4 \mathrm{mH}\)
- C \(0.8 \mathrm{mH}\)
- D \(0.6 \mathrm{mH}\)
Answer & Solution
Correct Answer
(A) \(0.2 \mathrm{mH}\)
Step-by-step Solution
Detailed explanation
At resonance, the impedance of the circuit is equal to resistance
\(
\therefore \mathrm{I}=\frac{\mathrm{V}_{\mathrm{R}}}{\mathrm{R}}=\frac{60}{120}=0.5 \mathrm{~A}
\)
Inductive reactance, \(X_L=\frac{V_L}{I}=\frac{40}{0.5}=80 \Omega\)
\(
\begin{aligned}
& \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L} \\
& \therefore \mathrm{L}=\frac{\mathrm{X}_{\mathrm{L}}}{\omega}=\frac{80}{4 \times 10^5}=20 \times 10^{-5} \mathrm{H} \\
& =0.2 \mathrm{mH}
\end{aligned}
\)
\(
\therefore \mathrm{I}=\frac{\mathrm{V}_{\mathrm{R}}}{\mathrm{R}}=\frac{60}{120}=0.5 \mathrm{~A}
\)
Inductive reactance, \(X_L=\frac{V_L}{I}=\frac{40}{0.5}=80 \Omega\)
\(
\begin{aligned}
& \mathrm{X}_{\mathrm{L}}=\omega \mathrm{L} \\
& \therefore \mathrm{L}=\frac{\mathrm{X}_{\mathrm{L}}}{\omega}=\frac{80}{4 \times 10^5}=20 \times 10^{-5} \mathrm{H} \\
& =0.2 \mathrm{mH}
\end{aligned}
\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The fundamental frequency of an air column in a pipe closed at one end is . If the same pipe is open at both the ends, the frequencies produced in areMHT CET 2017 Medium
- A step down transformer is used to reduce the main supply from ' \(V_1\) ' volt to ' \(V_2\) ' volt. The primary coil draws a current ' \(I_1\) ' A and the secondary coil draws ' \(I_2\) ' A. \(\left(I_1 < I_2\right)\). The ratio of input power to output power isMHT CET 2021 Medium
- An electron moving with velocity \(1.6 \times 10^7 \mathrm{~m} / \mathrm{s}\) has wavelength of \(0.4 Å\). The required accelerating voltage for the electron motion is [charge on electron \(=1.6 \times 10^{-19} \mathrm{C}\), mass of electron \(\left.=9 \times 10^{-31} \mathrm{~kg}\right]\)MHT CET 2023 Medium
- The ratio of weight of a man in a stationery lift and weight when the lift is moving downward with a uniform acceleration ' \(a\) ' is \(3: 2\). Then the value of ' \(a\) ' isMHT CET 2024 Medium
- If the frequency of incident light falling on a metallic surface is doubled, maximum kinetic energy of emitted photoelectronsMHT CET 2020 Easy
- The output of OR gate is ' 1 'MHT CET 2022 Easy
More PYQs from MHT CET
- If the slopes of the lines \(\mathrm{Kx}^2-4 \mathrm{xy}+5 \mathrm{y}^2=0\) differ by 2 , then \(\mathrm{K}=\)MHT CET 2022 Easy
- Arithmetic growth can be expressed mathematically by the formula Lt = Lo + rt, where Lt stands for ________.MHT CET 2025 Medium
- Threshold frequency for a metal is \(15 \times 10^{14} \mathrm{~Hz}\). The light of wavelength \(6000 Å\) falls on the metal surface. Which one of the following statements is correct? [velocity of light, \(\left.\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right]\)MHT CET 2020 Medium
- Let the r.m.s. velocity of molecule of a given mass of gas be \(\mathrm{C}_{1}\) at temperature \(27^{\circ} \mathrm{C}\). When the temperature is increased to \(327^{\circ} \mathrm{C}\), the \(\mathrm{r} . \mathrm{m} . \mathrm{s}\). velocity is \(\mathrm{C}_{2}\). Then the ratio \(\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}\) isMHT CET 2020 Easy
- A vector with magnitude of 3 units, which is perpendicular to each of the vectors \(\bar{a}=3 \hat{i}+\hat{j}-4 \hat{k}\) and \(\bar{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}\), is given byMHT CET 2022 Easy
- Select the mismatched pair with respect to mutated varieties of crops.MHT CET 2023 Medium