MHT CET · Physics · Alternating Current
A group of lamps having total power rating of \(1000 \mathrm{~W}\) is supplied by an \(\mathrm{AC}\) voltage of \(\mathrm{E}=200\) \(\sin \left(310 t+60^{\circ}\right)\), the r.m.s. value of current flowing through the circuit is
- A \(10 \mathrm{~A}\)
- B \(5 \sqrt{2} \mathrm{~A}\)
- C \(20 \mathrm{~A}\)
- D \(10 \sqrt{2} \mathrm{~A}\)
Answer & Solution
Correct Answer
(D) \(10 \sqrt{2} \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
Power:
\(\mathrm{P}=\frac{1}{2} \mathrm{~V}_0 \mathrm{I}_0 \cos \phi\)
\(\therefore \quad 1000=\frac{1}{2} \times 200 \times \mathrm{I}_0 \cos 60^{\circ}\)
\(\mathrm{I}_0=20 \mathrm{~A}\)
\(\therefore \quad \mathrm{I}_{\mathrm{mms}}=\frac{20}{\sqrt{2}}\)
\(\mathrm{I}_{\mathrm{rms}}=10 \sqrt{2} \mathrm{~A}\)
\(\mathrm{P}=\frac{1}{2} \mathrm{~V}_0 \mathrm{I}_0 \cos \phi\)
\(\therefore \quad 1000=\frac{1}{2} \times 200 \times \mathrm{I}_0 \cos 60^{\circ}\)
\(\mathrm{I}_0=20 \mathrm{~A}\)
\(\therefore \quad \mathrm{I}_{\mathrm{mms}}=\frac{20}{\sqrt{2}}\)
\(\mathrm{I}_{\mathrm{rms}}=10 \sqrt{2} \mathrm{~A}\)
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
- When the tension in string is increased by \(3 \mathrm{~kg} \omega \mathrm{t}\), the frequency of the fundamental mode increases in the ratio \(2: 3\). The initial tension in the string isMHT CET 2024 Medium
- If the momentum of a body of mass ' \(m\) ' is increased by \(20 \%\) then its kinetic energy increases byMHT CET 2024 Hard
- A current of \(5 \mathrm{~A}\) is flowing at \(220 \mathrm{~V}\) in the primary coil of transformer. If the voltage produced in the secondary coil is \(2200 \mathrm{~V}\) and \(50 \%\) of power is lost, then the current in secondary will beMHT CET 2022 Easy
- A series combination of \(n_1\) capacitors, each of value \(C_1\) is charged by a source of potential difference 6 V . Another parallel combination of \(\mathrm{n}_2\) capacitors, each of value \(\mathrm{C}_2\) is charged by a source of potential' difference 2 V . Total energy of both the combinations is same. The value of \(\mathrm{C}_2\) in terms of \(\mathrm{C}_1\) isMHT CET 2024 Hard
- A ray of light is incident on a medium of refractive index ' \(\mu\) ' at an angle of incidence ' \(i\) ': On refraction in the medium ' \(\delta\) ' is the angle of deviation. ThenMHT CET 2024 Medium
- A conducting sphere of radius ' \(R\) ' is given a charge ' \(Q\) ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ \(\epsilon_0=\) permittivity of free space]MHT CET 2025 Easy
More PYQs from MHT CET
- A compound has fcc structure. If density of unit cell is \(3 \cdot 4 \mathrm{~g} \mathrm{~cm}^{-3}\), what is the edge length of unit cell? (Molar mass \(=98.99\) )MHT CET 2020 Easy
- If the frequency of incident light in a photoelectric experiment is doubled, then stopping potential willMHT CET 2025 Medium
- In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged \((\mathrm{Q})\) is \(\left(\gamma=\frac{C_p}{C_v}\right)\)MHT CET 2024 Medium
- Which one of the following is a hormone releasing IUD?MHT CET 2021 Hard
- For athermanous substances, coefficient of transmission isMHT CET 2020 Easy
- What mass of solute (molar mass \(58 \mathrm{~g} \mathrm{~mol}^{-1}\) ) is to be dissolved in \(2.5 \mathrm{dm}^3 \mathrm{H}_2 \mathrm{O}\) to generate osmotic pressure of 0.245 atm at 300 K ? \(\left(\mathrm{R}=0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K} \mathrm{~mol}^{-1}\right)\).MHT CET 2024 Easy