Sinusoidal AC

Q. The equation of an alternating voltage is V =100 sin 100 $\pi$ t volt. Its peak value and frequency are

1. 50V, 100Hz
2. 100 V, 50 Hz
3. 100 V, 200 Hz
4. 200 V, 100 Hz

Q. A resistance of 20 ohms is connected to a source of an alternating potential $V=220sin\left(100\pi t\right)$. The time taken by the current to change from its peak value to r.m.s value is

1. $0.25sec$
2. $25\times {10}^{-3}sec$
3. $2.5\times {10}^{-3}sec$
4. $0.2sec$

Q. The peak value of an alternating e.m.f. E is given by $E=E_{0}cos\omega t$ is 10 volts and its frequency is 50 Hz. At time $t=\frac{1}{600}sec,$ the instantaneous e.m.f. is

1. $10V$
2. $5\sqrt{3}V$
3. $5V$
4. $1V$

Q.

The voltage of an ac source varies with time according to the equation $V=100sin100\pi tcos100\pi t$ where t is in seconds and V is in volts. Then

1. The peak voltage of the source is 100 volts
2. The peak voltage of the source is 50 volts
3. The frequency of the source is 50 Hz
4. The peak voltage of the source is $\frac{100}{\sqrt{2}}$ volts

Q. An ac voltage is represented by $E=220\sqrt{2}cos\left(50\pi \right)t$. The current becomes zero times in 1 sec.

1. 25
2. 50
3. 75
4. 100

Q. The peak value of an alternating emf is given by $E=E_{0}cos\left(wt\right)$ is 10 volt and its frequency is 50 Hz. At a time $t=\left(\frac{1}{600}\right)$ second, the instantaneous value of the emf is:

1. 1V
2. 5V
3. 10V
4. $5\sqrt{3}V$

Q. An ac generator produced an output voltage E = 170 sin 377 t volts, where t is in seconds. The frequency of ac voltage is

1. 50 Hz
2. 110 Hz
3. 60 Hz
4. 230 Hz

Q. Voltage and current in an ac circuit are given by $V=5sin(100\pi t-\frac{\pi }{6})$ and $I=4sin(100\pi t+\frac{\pi }{6})$

1. Voltage leads the current by ${30}^{\circ }$
2. Current leads the voltage by ${30}^{\circ }$
3. Current leads the voltage by ${60}^{\circ }$
4. Voltage leads the current by ${60}^{\circ }$

Q. An electric lamp is connected to 220 V, 50 Hz supply. Then the peak value of voltage is

1. 210 V
2. 311 V
3. 320 V
4. 211 V

Q. Voltage of an AC source is given by V= 200sin$\left(100\pi t\right).cos\left(100\pi t\right)$ where t is in seconds and V is in volts. Then the peak voltage is
volts.

1. 50
2. 100
3. 200
4. 400

Q. The voltage of an ac supply varies with time (t) as V = $120sin100\pi tcos100\pi t$ The maximum voltage and frequency respectively are

1. 60 volts, 100 Hz
2. 120 volts, 100 Hz
3. volts , 100 Hz
4. 60 volts, 200 Hz

Q. In an ac circuit, the current is given by $i=4\sin (100\pi t+{30}^{\circ })$ ampere. The first time when the current becomes maximum (after $t=0$) at $t$ is equal to -

Q. RMS current in a circuit of 50 Hz frequency is 5 A. Value of current $\frac{1}{300}$ seconds after its peak value is

1. $5\sqrt{\frac{3}{2}}$ A
2. 2.5 A
3. $5\sqrt{2}$ A
4. $\frac{5}{\sqrt{2}}$ A

Q. The voltage of an ac source varies with time according to the equation V = 200sin$\left(100\pi t\right).cos\left(100\pi t\right)$ where t is in seconds and V is in volts. Then

1. The peak voltage of the source is 100 volts
2. The peak voltage of the source is 50 volts
3. The frequency of the source is 50 Hz
4. The peak voltage of the source is 100 / √2 volts

Q.

An ac voltage is represented by $E=220\sqrt{2}cos\left(50\pi \right)t$ How many times will the current becomes zero in 1 s?

1. 50 times

2. 100 times

3. 30 times

4. 25 times

Q. An ac source is rated at 220V, 50 Hz. The time taken for voltage to change from its peak value to zero is

1. $5\times {10}^{-3}sec$
2. 0.02 sec
3. 5 sec
4. 50 sec

Q. What determines the frequency of a.c. produced in a generator?

1. The number of rotations of the coil in one second.
2. the speed of rotation of the coil
3. both A & B
4. None of the above

Q. The voltage of an ac supply varies with time (t) as $V=120sin100\pi tcos100\pi t$. The maximum voltage and frequency respectively are

1. 120 volts, 100 Hz
2. 60 volts, 200 Hz
3. 60 volts, 100 Hz
4. $\frac{120}{\sqrt{2}}volts,100Hz$

Q. If the phase difference between the emf and the current in an AC circuit is $f$ then the RMS value of wattless current will be

1. $I_{rms}cosf$
2. $I_{rms}sinf$
3. $I_{rms}tanf/2$
4. 0

Q. Match the following
$\begin{array}{cc}Currents& r.m.svalues\\ \left(1\right)x_{0}sin\omega t& \left(i\right)x_0\\ \left(2\right)x_{0}sin\omega tcos\omega t& \left(ii\right)\frac{x_0}{\sqrt{2}}\\ \left(3\right)x_{0}sin\omega t+x_{0}cos\omega t& \left(iii\right)\frac{x_0}{\left(2\sqrt{2}\right)}\end{array}$

1. 1. (i), 2. (ii), 3. (iii)
2. 1. (ii), 2. (iii), 3. (i)
3. 1. (i), 2. (iii), 3. (ii)
4. None of these

Q.

In the circuit given in the figure, switch S is closed at position 1 for long time. Find the total heat generated in resistor of resistance $2r_0$, when the switch S is open at position 1 and closed at position 2.

1. $\frac{C_0{E}_0^2}{4}$

2. $\frac{C_0{E}_0^2}{2}$

3. $C_0{E}_0^2$

4. $\frac{C_0{E}_0^2}{3}$

Q. An ac generator produced an output voltage E = 170 sin 377 t volts, where t is in seconds. The frequency of ac voltage is

1. 50 Hz
2. 110 Hz
3. 60 Hz
4. 230 Hz

Q. Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is 1 : 4 : 9 : 16, then the ratio of their fundamental frequencies are:

1. 16 : 9 : 4 : 1
2. 1 : 2 : 3 : 4
3. 4 : 3 : 2 : 1
4. 1 : 4 : 2 : 16

Q. A resistance of $20\Omega$ is connected to a source of an alternating potential $V=220\sin \left(100\pi t\right)$. The time taken by the current to change from the peak value to rms value, is

1. $0.2s$
2. $0.25s$
3. $2.5\times {10}^{-2}s$
4. $2.5\times {10}^{-3}s$

Q. Voltage and current in an ac circuit are given by $V=5sin(100\pi t-\frac{\pi }{6})$ and $I=4sin(100\pi t+\frac{\pi }{6})$

1. Voltage leads the current by ${30}^{\circ }$
2. Current leads the voltage by ${30}^{\circ }$
3. Current leads the voltage by ${60}^{\circ }$
4. Voltage leads the current by ${60}^{\circ }$

Q. An electric lamp is connected to 220 V, 50 Hz supply. Then the peak value of voltage is

1. 210 V
2. 211 V
3. 311 V
4. 320 V

Q. The equation of an alternating current is $I=50\sqrt{2}sin\left(400\pi t\right)$A, then the frequency and the root mean square value of the current respectively are

1. $200Hz,50A$
2. $400Hz$, $50\sqrt{2}A$
3. $200Hz$, $50\sqrt{2}A$
4. $500Hz,200A$

Q. A resistance of 20 ohms is connected to a source of an alternating potential $V=220sin\left(100\pi t\right)$. The time taken by the current to change from its peak value to r.m.s value is

1. $0.2sec$
2. $0.25sec$
3. $25\times {10}^{-3}sec$
4. $2.5\times {10}^{-3}sec$

Q. The instantaneous current from an a.c source is $I=5\sin 314t$. What is the (i) peak value (ii) r.m.s. value (iii) frequency of current?

Q. An alternating current is given by the equation $i=i_{1}cos\omega t+i_{2}sin\omega t$. The r.m.s. current is given by:

1. $\frac{1}{\sqrt{2}}(i_1+i_2)$
2. $\frac{1}{\sqrt{2}}(i_1+i_2{)}^2$
3. $\frac{1}{\sqrt{2}}(i_1^2+i_2^2{)}^{1/2}$
4. $\frac{1}{2}(i_1^2+i_2^2{)}^{1/2}$