Q. No.A \(40~\mu\text F\) capacitor is connected to a \(200~\text V,\) \(50~\text{Hz}\) AC supply. The RMS value of the current in the circuit is, nearly:
1.
\(2.05~\text A\)
2.
\(2.5~\text A\)
3.
\(25.1~\text A\)
4.
\(1.7~\text A\)
An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\dfrac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\dfrac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero
1. \(35\)
2. \(20\)
3. \(15\)
4. \(25\)
At a hydroelectric power plant, the water pressure head is at a height of \(300\) m and the water flow available is \(100\) m3 s-1. If the turbine generator efficiency is \(60\)%, the electric power available from the plant is:
(Take \(g=9.8\) m s-2)
1. \(111.3\) MW
2. \(210\) MW
3. \(176.4\) MW
4. \(213.5\) MW
A direct current of \(5~ A\) is superimposed on an alternating current \(I=10sin ~\omega t\) flowing through a wire. The effective value of the resulting current will be:
| 1. | \(15/2~A\) | 2. | \(5 \sqrt{3}~A\) |
| 3. | \(5 \sqrt{5}~A\) | 4. | \(15~A\) |
An AC ammeter is used to measure the current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads \(6~\text A.\) When another alternating current passes through the circuit, the AC ammeter reads \(8~\text A.\) Then the reading of this ammeter if DC and AC flow through the circuit simultaneously is:
1. \(10 \sqrt{2}~\text A\)
2. \(14~\text A\)
3. \(10~\text A\)
4. \(15~\text A\)
The time required for a \(50\text{ Hz}\) sinusoidal alternating current to change its value from zero to the rms value will be:
1. \(1 . 5 \times 10^{- 2}~\text{s}\)
2. \(2 . 5 \times 10^{- 3}~\text{s}\)
3. \(10^{- 1}~\text{s} \)
4. \(10^{- 6}~\text{s}\)
1. \(\dfrac{1}{20}~\text{A}\)
2. zero
3. \(\dfrac{1}{10}~\text{A}\)
4. \(\dfrac{1}{5}~\text{A}\)
| Assertion (A): | When a current \(I=(3+4 \sin \omega t)\) flows in a wire, then the reading of a dc ammeter connected in series is \(4\) units. |
| Reason (R): | A dc ammeter measures only the value of the current amplitude. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
In a box \(Z\) of unknown elements (\(L\) or \(R\) or any other combination), an ac voltage \(E = E_0 \sin(\omega t + \phi)\) is applied and the current in the circuit is found to be \(I = I_0 \sin\left(\omega t + \phi +\frac{\pi}{4}\right)\). The unknown elements in the box could be:
| 1. | Only the capacitor |
| 2. | Inductor and resistor both |
| 3. | Either capacitor, resistor, and an inductor or only capacitor and resistor |
| 4. | Only the resistor |
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