RMS Value

Q.

A 50 Hz a.c. is rectified with full wave rectifier, what is the output frequency?

1. 50

2. 100

3. 25

4. 200

Q.

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10¹⁰ Hz and amplitude 48 V m⁻¹.

(a) What is the wavelength of the wave?

(b) What is the amplitude of the oscillating magnetic field?

(c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 × 10⁸ m s⁻¹.]

Q. The electric current in circuit is given by $I=I_o\left(\frac{t}{T}\right)$ some time. What is the rms current for the period $t=0$ to $t=T$?

1. $\frac{I_0}{\sqrt{3}}$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{\sqrt{2}}$
4. $\frac{I_0}{3}$

Q. A $100\Omega$ resistance, a $0.1\mu F$ capacitor and an inductor are connected in series across a $250\text{V}$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will ocur. Given that the resonant frequency is $60\text{Hz}$

1. $0.70\text{H}$
2. $70.4\text{mH}$
3. $7.03\times {10}^{-5}\text{H}$
4. $70.4\text{H}$

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. The frequency of an alternating voltage is 50 cycles/sec and its amplitude is 120V. Then the r.m.s. value of voltage is

1. 101.3V
2. 84.8V
3. 70.7V
4. 56.5V

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. 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

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. The maximum value of a.c. voltage in a circuit is 707V. Its rms value is

1. 100 V
2. 70.7 V
3. 500 V
4. 707 V

Q. If $I_1,I_2,I_3$ and $I_4$ are the respective r.m.s. values of the time varying currents as shown in the four cases $\text{I, II, III}$ and $\text{IV}$. Then identify the correct relations.

1. $I_2>I_1$
2. $I_3>I_4$
3. $I_1>I_4$
4. $I_1=I_2$

Q. Calculate the $rms$ value of the $emf$ for a cycle, whose time variation is shown in figure.

1. $V_0$
2. $\frac{V_0}{2}$
3. $\frac{2V_0}{3}$
4. $\frac{V_0}{\sqrt{2}}$

Q. A 100 W resistor is connected to a 220 V, 50 Hz ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed over a full cycle?

Q.

An AC current is given by$I=I_1\sin \omega t+I_2\cos \omega t$. A hot wire ammeter will give a reading :

1. $\begin{array}{l}\frac{I_1+I_2}{\sqrt{2}}\end{array}$

2. $\begin{array}{l}\sqrt{\frac{I_1^2+I_2^2}{2}}\end{array}$

3. $\begin{array}{l}\sqrt{\frac{I_1^2-I_2^2}{2}}\end{array}$

4. $\begin{array}{l}\frac{I_1+I_2}{2\sqrt{2}}\end{array}$

Q. $m,e,{\epsilon }^{0}h\text{and}c$ denote mass electron, charge of electron, Planck's constant and speed of light, respectively. The dimensions of $\frac{{\text{me}}^4}{{\epsilon }_0^2{\text{h}}^3\text{c}}$ are

1. $\left[M^0{L}^0{T}^{-1}\right]$
2. $\left[M^0{L}^{-1}{T}^0\right]$
3. $\left[M^0{L}^{-1}{T}^{-1}\right]$
4. $\left[{\text{M}}^2{\text{LT}}^{-3}\right]$

Q. An inductor coil, a capacitor and an A.C source of rms voltage 24 V are connected in series. When the frequency of the source is varied, a maximum rms current of 6 A is observed. If this inductor coil is connected to a battery of emf 12V and internal resistance of $4\Omega$, what is the steady current.(Write upto two digits after the decimal point.)

Q. Find the average current for the time interval $t=-1$ to $t=1\text{s}$, if the current is given by, $i=(6t^5+3t^2+1)\text{A}$.

1. $1\text{A}$
2. $0.5\text{A}$
3. $3\text{A}$
4. $2\text{A}$

Q. In the circuit, switch $S$ is closed at time $t=0$, Let $I_1$ and $I_2$ be the currents at any finite time $t$, then the ratio of $\frac{I_1}{I_2}$

1. is constant
2. increases with time
3. decreases with time
4. first increases, then decreases

Q.

Power dissipation is maximum in

1. Pure capacitive circuit

2. Pure inductive circuit

3. Pure resistive circuit

4. None of these

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. For the waveform given below


The $\text{rms}$ value of the wave form is given by

1. $10\sqrt{7}$
2. $\frac{10}{\sqrt{3}}$
3. $10\sqrt{\frac{7}{3}}$
4. $10\sqrt{3}$

Q. Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?

Q. A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$, it has the same (total) energy stored in it, as the first combination has. The value of $C_2$, in terms of $C_1$, is then

1. $\frac{16C_1}{n_1{n}_2}$
2. $\frac{2C_1}{n_1{n}_2}$
3. $2\frac{n_2}{n_1}{C}_1$
4. $16\frac{n_2}{n_1}{C}_1$

Q. A charged $30\mu \text{F}$ capacitor is connected to a $27\text{mH}$ inductor. Suppose the initial charge on the capacitor is $6\text{mC}$. What is the total energy stored in the circuit initially? What is the total energy at later time?

Q.

What is the potential difference across any of the electric home appliances? What does it indicate?

Q. If a direct current of $3\text{A}$ is superimposed on an alternating current $i=4\sqrt{2}\sin \omega t\text{A}$, flowing through a wire, what is the average value of current in one complete cycle ?

1. $5\text{A}$
2. $4\sqrt{2}\text{A}$
3. $3\text{A}$
4. $(3+4\sqrt{2})\text{A}$

Q. a) The peak voltage of an ac supply is 300 V. What is the rms voltage? (b) The rms value of current in an ac circuit is 10 A. What is the peak current?

Q. In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3}{m}^2$ and the distance between the plates is $3mm$. Calculate the capacitance of the capacitor. If this capacitor is connected to a $100V$ supply, what is the charge on each plate of the capacitor?

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. The tuning circuit of a radio receiver has a resistance of $50\Omega$, an inductor of $10\text{mH}$ and a variable capacitor. A $1\text{MHz}$ radio wave produces a potential difference of $0.1\text{mV}.$ The value of the capacitor to produce the resonance is $($take${\pi }^2=10)$

1. $50\text{pF}$
2. $25\text{pF}$
3. $5.0\text{pF}$
4. $2.5\text{pF}$