Electromagnetic Induction and Alternating Currents
- An inductor 20 mH, a capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is Answer: 1. 0.79 W Power is lost only in the resistor: P=I_rms²R , with I_rms=V_rms/Z . X_L=ω L=314×0.02=6.28\ Ω ; X_C=1/ω C=dfrac1314×10⁻⁴=3... 1
- A long solenoid of diameter 0.1 m has 2×10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A… Answer: 2. 32 μ C Key idea: charge q=ΔΦ/R (independent of the time taken). Field inside solenoid B=μ₀nI . Change: Δ B=4π×10⁻⁷×2×10⁴×4=0.032π... 1
- Figure shows a circuit that contains three identical resistors with resistance R = 9.0 Ω each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf ε = 18 V. The current 'i' through the battery just after the switch… Answer: Dropped in the official answer key: full marks to every candidate Key idea: just after the switch closes, an inductor acts as an ope... 1
- A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate d B/dt. Loop 1 of radius R>r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figur… Answer: 3. -dvec B/dtπ r² in loop 1 and zero in loop 2 Induced emf is -dΦ/dt , and flux counts only the area where the field exists. Loop 1... 1
- The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is Answer: 2. 0.8 Power factor cosφ=V_R/V , where V is the supply voltage. V_L-V_C=100-40=60 V. V=√(V_R²+(V_L-V_C)²)=√(80²+60²)=100 V. cosφ=80/... 1
- Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication? Answer: 2. R=15\ Ω , L=3.5 H, C=30\ μ F Good tuning means a sharp resonance, i.e. a high quality factor Q=1/R√(L/C) . Option √(L/C) ( Ω ) Q... 1
- A 100 Ω resistance and a capacitor of 100 Ω reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is Answer: 4. 2.2 A Displacement current in the capacitor gap equals the conduction current in the circuit at every instant, so its peak is the... 1
- A small signal voltage V(t) = V_0 ω t is applied across an ideal capacitor C : Answer: 2. Over a full cycle the capacitor C does not consume any energy from the voltage source. Key idea: in an ideal capacitor, current l... 1
- An inductor 20 mH, a capacitor 50 μF and a resistor 40 Ω are connected in series across a source of emf V = 10 340 t. The power loss in A.C. circuit is : Answer: 1. 0.51 W Key idea: average power P=I_rms²R , with I_rms=V_rms/Z . X_L=ω L=340×0.02=6.8\ Ω ; X_C=dfrac1ω C≈58.8\ Ω . Z=√(40²+52²)=√(... 1
- A long solenoid has 1000 turns. When a current of 4A flows through it, the magnetic flux linked with each turn of the solenoid is 4×10^-3 Wb. The self-inductance of the solenoid is : Answer: 4. 1 H Key idea: L=Nφ/I , where φ is the flux per turn. L=dfrac1000×4×10⁻³4=1 H. 1