RMS Value

Q. A $\text{LCR}$ series combination is connected to an $\text{AC}$ source. If voltages across the inductor, capacitor, resistor are $40V,80V$ and $40V$ respectively. Then the voltage across the $\text{AC}$ source is $x\sqrt{2}\text{V}$. Find $x$

Q. The rms value of an alternating current, which when passed through a resistor produces heat three times of that produced by a direct current of 2A in the same resistor, is

1. 6A
2. 3A
3. 2A
4. 2$\sqrt{3}$A

Q.

In a certain circuit current changes with time according to $i=2\sqrt{t}.$ r.m.s. value of current between t=2 to t=4s will be

1. 3A

2. 
   

3. 
   

4. 
   

Q. A 220 V main supply is connected to a resistance of 100k $\Omega$ . The rms current is

1. 22 mA
2. 2.2mA
3. 220mA
4. 10 mA

Q. In a certain circuit current changes with time according to i = 2$\sqrt{t}$ r.m.s. value of current between t = 2 to t = 4s will be

1. 3A
2. 3√3 A
3. 2√3 A
4. (2 - √2)A

Q. A 280 ohm electric bulb is connected to 200V electric line. The peak value of current in the bulb will be

1. About four ampere
2. About one ampere
3. Zero
4. About two ampere

Q. The r.m.s. voltage of domestic electricity supply is 220 volt . Electrical appliances should be designed to withstand an instantaneous voltage of

1. 220 V
2. 310 V
3. 330 V
4. 440 V

Q. Match the following

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

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

Q. The r.m.s. value of an ac of 50 Hz is 10 amp. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be

1. $2\times {10}^{-2}$ sec and 14.14 amp
2. $1\times {10}^{-2}$ sec and 7.07 amp
3. $5\times {10}^{-3}$ sec and 7.07 amp
4. $5\times {10}^{-3}$ sec and 14.14 amp

Q. In a circuit, the value of the alternating current is measured by hot wire ammeter as 10 ampere. Its peak value will be

1. 10 A
2. 20 A
3. 14.14 A
4. 7.07 A