Alternating Current - Live Session - 04 Oct 2020Contact Number: 9667591930 / 8527521718

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The potential difference *V* and the current *i* flowing through an instrument in an ac circuit of frequency *f* are given by $V=5\mathrm{cos}\omega \text{\hspace{0.17em}}t$ *volts *and *I* = 2 sin *ωt* *amperes* (where *ω* = 2*πf*). The power dissipated in the instrument is

(1) Zero

(2) 10 *W*

(3) 5 *W*

(4) 2.5 *W*

A generator produces a voltage that is given by *V* = 240 sin 120 *t*, where *t* is in seconds. The frequency and *r.m.s*. voltage are** **

(1) 60 *Hz* and 240 V

(2) 19 *Hz* and 120 V

(3) 19 *Hz* and 170 V

(4) 754 *Hz* and 70 V

An alternating current is given by the equation $i={i}_{1}\mathrm{cos}\omega \text{\hspace{0.17em}}t+{i}_{2}\mathrm{sin}\omega \text{\hspace{0.17em}}t$. The *r.m.s*. current is given by

(1) $\frac{1}{\sqrt{2}}({i}_{1}+{i}_{2})$

(2) $\frac{1}{\sqrt{2}}{({i}_{i}+{i}_{2})}^{2}$

(3) $\frac{1}{\sqrt{2}}{({i}_{1}^{2}+{i}_{2}^{2})}^{1/2}$

(4) $\frac{1}{2}{({i}_{1}^{2}+{i}_{2}^{2})}^{1/2}$

1. | \( 0.2~\text{sec}\) | 2. | \( 0.25~\text{sec}\) |

3. | \(25 \times10^{-3}~\text{sec}\) | 4. | \(2.5 \times10^{-3}~\text{sec}\) |

Voltage and current in an ac circuit are given by $V=5\mathrm{sin}\text{\hspace{0.17em}}\left(100\pi t-\frac{{\displaystyle \pi}}{{\displaystyle 6}}\right)$ and $I=4\mathrm{sin}\text{\hspace{0.17em}}\left(100\pi t+\frac{{\displaystyle \pi}}{{\displaystyle 6}}\right)$

(1) Voltage leads the current by 30°

(2) Current leads the voltage by 30°

(3) Current leads the voltage by 60°

(4) Voltage leads the current by 60°

1. \(R + 2\pi f L\)

2. \(\sqrt{R^{2} + 4 \pi^{2} f^{2} L^{2}}\)

3. \(\sqrt{R^{2} + L^{2}}\)

4. \(\sqrt{R^{2} + 2 \pi f L}\)

A resistance of \(300~\Omega\) and an inductance of \(\frac{1}{\pi}\) henry are connected in series to an AC voltage of \(20\) volts and a \(200\) Hz frequency. The phase angle between the voltage and current will be:

1. \(\tan^{- 1} \frac{4}{3}\)

2. \(\tan^{- 1} \frac{3}{4}\)

3. \(\tan^{- 1} \frac{3}{2}\)

4. \(\tan^{- 1} \frac{2}{5}\)

In a region of uniform magnetic induction *B* = 10^{–2} *tesla*, a circular coil of radius 30 *cm* and resistance *π*^{2} *ohm* is rotated about an axis that is perpendicular to the direction of *B* and which forms a diameter of the coil. If the coil rotates at 200 *rpm* the amplitude of the alternating current induced in the coil is** :**

(1) 4*π*^{2} *mA*

(2) 30 *mA*

(3) 6 *mA*

(4) 200 *mA*

1. | \(\frac{R}{4}\) |

2. | \(\frac{R}{2}\) |

3. | \(R\) |

4. | Cannot be found with the given data |

In a series *LCR* circuit, resistance *R *= 10*Ω* and the impedance *Z *= 20*Ω*. The phase difference between the current and the voltage is

(1) 30°

(2) 45°

(3) 60°

(4) 90°

In the circuit shown below, the AC source has voltage \(V = 20\cos(\omega t)\) volts with \(\omega =2000\) rad/sec. The amplitude of the current is closest to:

** **

1. \(2\)* *A

2. \(3.3\)* *A

3. $\mathrm{}$\(\frac{2}{\sqrt{5}}\)

4. \(\sqrt{5}~\text{A}\) $$

An inductor of inductance \(L\) and resistor of resistance \(R\) are joined in series and connected by a source of frequency \(\omega\).
The power dissipated in the circuit is:

1. \(\frac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\)

2. \(\frac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\)

3. \(\frac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\)

4. \(\frac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}\)

In an \(LCR\) circuit, the potential difference between the terminals of the inductance is \(60\) V, between the terminals of the capacitor is \(30\) V and that between the terminals of the resistance is \(40\) V. The supply voltage will be equal to:

1. \(50\) V

2. \(70\) V

3. \(130\) V

4. \(10\) V

One 10 *V*, 60 *W* bulb is to be connected to 100 *V* line. The required induction coil has a self-inductance of value: (*f* = 50 Hz)** **

(1) 0.052 *H*

(2) 2.42 *H*

(3) 16.2 *mH*

(4) 1.62 *mH*

In the circuit shown below, what will be the readings of the voltmeter and ammeter?

** **

1. \(800~\text{V}, 2~\text{A}\)

2. \(300~\text{V}, 2~\text{A}\)

3. \(220~\text{V}, 2.2~\text{A}\)

4. \(100~\text{V}, 2~\text{A}\)

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