Reactance, impedance, LCR series circuit, resonance
- 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... 1
- 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 ,... 1
- 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... 1
- 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... 1
- 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... 1
- 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... 1
- 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+... 1
- 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... 1
- 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... 1
- 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. 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
- 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
- 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
- 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 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