# RMS Value of Current in Sinusoidal AC

## Trending Questions

**Q.**In an AC circuit, the current is given by I=4sin(100πt+30∘) A. The current becomes maximum for the first time (After t=0) at t equal to

- 1200 s
- 1300 s
- 150 s
- 1100 s

**Q.**A small square loop of wire of side l is placed inside a large square loop of side L (l<<L). The loops are co-planar and their centres coincide. The mutual induction of the system is proportional to

- lL
- l2L
- Ll

- L2l

**Q.**The peak voltage in a 220 V AC source is -

Take √2=1.414

- 220 V
- 320 V
- 311 V
- 430 V

**Q.**In an AC circuit, the current is given by the equation, i=2√13sin(50πt) A. Calculate the time taken to reach from zero (at t=0) to its first maximum value.

- 5 ms
- 10 ms
- 20 ms
- 100 ms

**Q.**The alternating current is given by i={√42sin(2πTt)+10} A. The r.m.s value of this current is

**Q.**The magnetic flux in a closed circuit, of resistance 20 Ω, varies with time (t) according to the equation ϕ=7t2−4t. Where ϕ is in webers and t is in seconds. The magnitude of the induced current at t=0.25 sec is,

- 0.25 A
- 0.025 A
- 50 mA
- 175 mA

**Q.**

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

**Q.**For the circuit shown, the value of current at time t=3.2 s will be

[Voltage distribution V(t) is shown by Figure 1 and the circuit is shown in Figure 2]

**Q.**

The instantaneous voltages at three terminals marked X, Y and Z are given by

VX=V0sinωt

VY=V0sin(ωt+2π3) and

VZ=V0sin(ω0+4π3)

An ideal voltmeter is configured to read rms of the value of potential difference between its terminals. It is connected between points points X and Y and then between Y and Z. The reading (S) of the voltmeter will be

- (VXY)rms=Vo√32
- (VYZ)rms=Vo√12
(VXY)rms=Vo

Independent of the choice of the two terminals

**Q.**A 10 Ω resistance is connected across 220 V–50 Hz AC supply. The time taken by the current to change from its maximum value to the RMS value is

- 2.5 ms
- 1.5 ms
- 4.5 ms
- 3.0 ms

**Q.**The magnetic flux through a stationary loop with resistance R varies during an interval of time T as ϕ=at(T−t). The heat generated during this time neglecting the inductance of the loop will be

- a2T33R
- a2T23R
- a2T3R
- a3T23R

**Q.**Find the average value of current (in A) as shown graphically in the figure, from t=0 to t=2 s.

**Q.**

The household supply of electricity is at 220 V (rms value) and 50 Hz. Find the peak voltage and the least possible time in which the voltage can change from the rms value to zero

**Q.**Determine the rms value of a semi-circular current wave which has a maximum value of a Ampere. The y axis denotes current in Ampere and x axis denotes time.

- (1√2)a
- √32a
- √23a
- √13a

**Q.**The magnetic field through a single loop of wire having radius 12 cm and resistance 8.5 Ω changes with time as shown in the figure. The magnetic field is perpendicular to the plane of the loop. Plot the induced current as a function of time.

**Q.**In an AC generator, a coil with N turns, all of them has same area A and total resistance R, rotates with an angular frequency ω in a magnetic field B. The peak value of current in the coil is-

- NBAωR
- NBAR
- NBAωsinωtR
- NBAωcosωtR

**Q.**A conducting circular loop of face area 2.5×10−3 m2 is arranged with its plane perpendicular to a magnetic field which varies as B=0.20sin(50πt). Find the net charge flowing through the loop during the interval t=0 to t=40 ms.

Assume resistance of the loop to be 10 Ω.

- 1 C
- 0.5 C
- 0.25 C
- Zero

**Q.**An AC source is rated 220 V, 50 Hz. The average voltage, is calculated in a time interval of 0.01 s. It

- must be zero
- is never zero
- may be zero
- must be infinite

**Q.**If a direct current of value a ampere is superimposed on an alternating current I=bsinωt flowing through a wire, what is the effective value of the resulting current in the circuit?

- √a2+b2
- √a2+b24
- √a2+b22
- √a22+b2

**Q.**A circular coil of radius 5 cm, has 500 turns of a conducting wire. The approximate value of the coefficient of self induction of the coil will be -

- 25 mH
- 5 mH
- 0.5 mH
- 2.5 mH

**Q.**An alternating voltage, V=60sin(πt) is applied across a 20 Ω resistor. What will be the reading of an AC ammeter, connected in series with the resistor?

- 3 A
- 3√2 A
- 1.5 A
- The reading of ammeter will change with time.

**Q.**Two neighbouring coils A and B have a mutual inductance of 20 mH. The current flowing through A is given by i=3t2−4t+6. The induced emf at t=2s in coil B is-

- 160 mV
- 200 mV
- 260 mV
- 300 mV

**Q.**A closed coil having 50 turns, area 300 cm2, is rotated from a position where its plane makes an angle of 60∘ with a magnetic field of flux density 2.0 T to a position perpendicular to the field in a time of 10 s. What is the average emf induced in the coil?

**Q.**Two coils P and Q are separated by some distance. When a current of 3 A flows through coil P, a magnetic flux of 10−3 Wb passes through Q. No current is passed through Q. When no current passes through P and a current of 2 A passes through Q. The flux through P is-

- 6.67×10−4 Wb
- 3.67×10−4 Wb
- 6.67×10−3 Wb
- 3.67×10−3 Wb

**Q.**Calculate the inductance per unit length of a double tape line as shown in the figure. The tapes are separated by a distance h which is considerably less than their width b.

- μ0hb
- μ0h2b
- 2μ0hb
- √2μ0hb

**Q.**A conducting loop of area 5 cm2 is placed in a magnetic field which varies sinusoidally with time as B=0.2sin300t. The normal to the coil makes an angle of 60∘ with the field. The emf induced at t=π900 s, is

- 7.5×10−3 V
- Zero
- 15×10−3 V
- 20×10−3 V

**Q.**Consider a long wire carrying a time varying current i=kt (k>0). A circular loop of radius a and resistance R is placed with its center at a distance d from the wire (a<<d). The induced current in the loop is

- μ0a2k4dR
- μ0d2k2aR
- μ0a2k2dR
- μ0(a+d)2k2aR

**Q.**An alternating current is given by the equation, i=3√2sin(100πt+π/4) and an alternating voltage is given by the equation, E=220√2sin(100πt+π/2). Calculate the phase difference between them.

- π/4
- π/3
- π/2
- π/6

**Q.**Magnetic flux ϕ (in Webers) linked with a closed circuit of resisitance 100 Ω varies with time t (in seconds) as ϕ=5t2−4t+1. The induced current in the circuit at t=0.2 sec is

- 5 mA
- 10 mA
- 20 mA
- 1 A

**Q.**

A plane loop is shaped in the form as shown in figure with radii a=20 cm and b=10 cm and is placed in a uniform time varying magnetic field B=B0 sinω t , where B0=10 mT and ω=100rad/s. Find the amplitude of the current induced(in A) in the loop, if its resistance per unit length is equal to 50×10−3Ωm. The inductance of the loop is negligible.