Electromagnetic Induction and Alternating Currents

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To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is,… Answer: 2. 7.8 A and 45^° Key idea: in a series LCR circuit, Z=√(R²+(X_L-X_C)²) and tanφ=X_L-X_C/R . X_L-X_C=45-25=20\ Ω, Z=√(20²+20²)=20sqr... Reactance, impedance, LCR series circuit, resonance 1 answer
AB is a part of an electrical circuit (see figure). The potential difference "V_A - V_B", at the instant when current i = 2 A and is increasing at a rate of 1 amp / second is: Answer: 4. 10 volt Key idea: going from A to B, add the potential change across each element. The current flows from A to B and is increasin... Self and mutual inductance 1 answer
A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to :A. hold the sheet there if it is magnetic.B. hold the sheet there if it is non-magnetic.C. move the sheet away from the pole with uniform velocity if… Answer: 3. A and C only Key idea: A force is needed only if the magnetic pole exerts a force on the sheet. A: A magnetic sheet is attracted... Lenz's law and eddy currents 1 answer
A 10 μ F capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly (π=3.14): Answer: 3. 0.93 A Key idea: For a capacitor in an AC circuit the capacitive reactance is X_C=1/ω C and the peak current is I₀=V₀/X_C=V₀ω C ,... Reactance, impedance, LCR series circuit, resonance 1 answer
In an ideal transformer, the turns ratio is N_p/N_s=1/2. The ratio V_s : V_p is equal to (the symbols carry their usual meaning) : Answer: 3. 2 : 1 Key idea: For an ideal transformer V_s/V_p=N_s/N_p . Given N_p/N_s=1/2 , we get N_s/N_p=2 , so V_s:V_p=2:1 . It is a step-u... AC generator and transformer 1 answer
In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions: Answer: 2. AB and DC Key idea: Lenz's law: the induced current opposes the change in flux, so a solenoid end facing a moving magnet behaves... Lenz's law and eddy currents 1 answer
In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω. The frequency at which resonance occurs is : Answer: 1. 1.59 kHz Resonance occurs when X_L=X_C : f₀=1/2π√(LC) . Resistance does not affect it. LC=10×10⁻³×10⁻⁶=10⁻⁸ , so √(LC)=10⁻⁴ s. f₀... Reactance, impedance, LCR series circuit, resonance 1 answer
An ac source is connected to a capacitor C. Due to decrease in its operating frequency : Answer: 4. displacement current decreases. Capacitive reactance X_C=1/2π fC . When the frequency decreases, X_C increases. The current (and... Reactance, impedance, LCR series circuit, resonance 1 answer
The net impedance of circuit (as shown in figure) will be : Answer: 4. 5√(5) Ω For a series LCR circuit Z=√(R²+(X_L-X_C)²) . X_L=2π fL=2π(50)50/π×10⁻³=5 Ω . X_C=1/2π fC=dfrac12π(50)10³/π×10⁻⁶=10 Ω . Z... Reactance, impedance, LCR series circuit, resonance 1 answer
The magnetic energy stored in an inductor of inductance 4 μH carrying a current of 2 A is : Answer: 1. 8 μ J Energy stored in an inductor: U=1/2LI² . U=1/2×(4×10⁻⁶)×(2)² = 8×10⁻⁶ J = 8 μ J. Self and mutual inductance 1 answer
A 12 V, 60 W lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding? Answer: 2. 0.27 A An ideal transformer has no loss, so input power equals output power. Output power = 60 W, so V_pI_p = 60⇒ I_p=60/220≈ 0.2... AC generator and transformer 1 answer
A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s^-1. If the vertical component of earth's magnetic field at that place is 2 × 10^-5 T and electrical resistance of the coil is 12.56 Ω, then… Answer: 4. 1 A Maximum emf in a rotating coil is ε_max=NBAω , with the field component perpendicular to the axis (vertical component here).... Faraday's law, induced emf and current 1 answer
A series LCR circuit with inductance 10 H, capacitance 10 μF, resistance 50 Ω is connected to an ac source of voltage, V = 200 (100 t) volt. If the resonant frequency of the LCR circuit is _0 and the frequency of the ac source is , then : Answer: 3. ν₀ = ν = 50/π Hz Compare the source frequency with the resonant frequency. Source: ω=100\ rad/s⇒ν=100/2π=50/π Hz. Resonance: ω₀=1... Reactance, impedance, LCR series circuit, resonance 1 answer
The peak voltage of the ac source is equal to : Answer: 4. √(2) times the rms value of the ac source For a sinusoidal ac, V_rms=V₀/sqrt2 , so the peak value is V₀=sqrt2 V_rms . Option (4)... AC peak and RMS values 1 answer
A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is : Answer: 3. 0.5 weber Flux is φ=BAcosθ . The plane of the loop is perpendicular to the field, so the normal is parallel to B and θ=0 . φ=0.5×... Faraday's law, induced emf and current 1 answer
A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ? Answer: 1. 0.2 A Key idea: with no losses, input power = output power = 44 W. I_p=P/V_p=44/220=0.2 A. Option 1. (The secondary current is 44... AC generator and transformer 1 answer
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in figure.Potential difference across L, C and R is 40 V, 10 V and 40 V, res… Answer: 4. 5\ Ω Key idea: voltages in series LCR add as phasors: V=√(V_R²+(V_L-V_C)²) , and Z=V/I with both in the same (rms) form. V=√(40²+... Reactance, impedance, LCR series circuit, resonance 1 answer
A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant an… Answer: 3. 46 rad/s and 54 rad/s Key idea: power falls to half of its resonance value when |X_L-X_C|=R , which happens at ω=ω₀±dfrac R2L (fo... Reactance, impedance, LCR series circuit, resonance 1 answer
Two conducting circular loops of radii R_1 and R_2 are placed in the same plane with their centres coinciding. If R_1 >> R_2, the mutual inductance M between them will be directly proportional to : Answer: 4. R₂²/R₁ Key idea: the large loop R₁ produces a nearly uniform field at its centre, which passes through the small loop. B=μ₀I/2R₁... Self and mutual inductance 1 answer
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and vo… Answer: 3. 1.0 With L removed, the circuit is RC: tanφ=X_C/R . With C removed, it is RL: tanφ=X_L/R . Both phase angles are π/3 , so X_C=X_L... Reactance, impedance, LCR series circuit, resonance 1 answer
A 40 μF capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly : Answer: 3. 2.5 A Capacitive reactance X_C=1/2π fC . X_C=frac12π×50×40×10⁻⁶≈79.6\ Ω I_rms=fracV_rmsX_C=200/79.6≈2.5\ A Answer: option 3. Reactance, impedance, LCR series circuit, resonance 1 answer
A 800 turn coil of effective area 0.05 m^2 is kept perpendicular to a magnetic field 5×10^-5 T. When the plane of the coil is rotated by 90^° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be : Answer: 4. 0.02 V The coil starts perpendicular to the field (flux =NBA ) and, after rotating 90^° , lies parallel to it (flux zero). ε=Δφ/Δ... Faraday's law, induced emf and current 1 answer
In which of the following devices, the eddy current effect is not used ? Answer: 3. electromagnet or 4. electric heater Eddy currents are induced in a conductor by a changing magnetic flux. Induction furnace: eddy... Lenz's law and eddy currents 1 answer
The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance Answer: 4. 13.89 H Energy stored in an inductor: U=1/2LI² . L=2U/I²=frac2×25×10⁻³(60×10⁻³)²=frac0.053.6×10⁻³≈13.89\ H Self and mutual inductance 1 answer

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