Reactance, impedance, LCR series circuit, resonance
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See all →- 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