An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)

A 50 Hz a.c. source of 20 volts is connected across R and C as shown in the figure below. If the voltage across R is 12 volts, then the voltage across C will be:
   

What is the value of inductance L for which the current is a maximum in a series LCR circuit with C=10 μF and $\mathrm{\omega }$ = 1000 s^-1?

Alternating current cannot be measured by a D.C. ammeter because:

For a LCR series circuit with an A.C. source of angular frequency $\mathrm{\omega :}$

In an L-R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf of E = E₀cos(ωt) is applied to the circuit. The power consumed by the circuit is:

1. $\frac{{\mathrm{E}}_0^2}{\sqrt{2}\mathrm{R}}$

2. $\frac{{\mathrm{E}}_0^2}{4\mathrm{R}}$

3. $\frac{{\mathrm{E}}_0^2}{2\mathrm{R}}$

4. $\frac{{\mathrm{E}}_0^2}{8\mathrm{R}}$

A series AC circuit has a resistance of 4 $\mathrm{\Omega }$ and an inductor of reactance 3 $\mathrm{\Omega }$. The impedance of the circuit is z₁. Now when a capacitor of reactance 6 $\mathrm{\Omega }$ is connected in series with the above combination, the impedance becomes $z_{2.}$ $\frac{{\mathrm{z}}_1}{{\mathrm{z}}_2}$ will be:

1. 1 : 1

2. 5 : 4

3. 4 : 5

4. 2 : 1

An inductor (L) and resistance (R) are connected in series with  an AC source. The phase difference between voltage (V) and current (i) is $45°$. If the phase difference between V and i remains the same, then the capacitive reactance and impedance of the L-C-R circuit will be:

1. 2R, R$\sqrt{2}$

2. R, R$\sqrt{2}$

3. R, R

4. 2R, R$\sqrt{3}$

An \(AC\) voltage is applied to a resistance \(R\) and an inductor \(L\) in series. If \(R\) and the inductive reactance are both equal to \(3~ \Omega, \) then the phase difference between the applied voltage and the current in the circuit will be:

A coil of self-inductance L is connected in series with a bulb B and an AC source. The brightness of the bulb decreases when: