Impedance Triangle

Q. Which of the following combination should be selected for better tuning of an LCR circuit used for communication?

1. $R=25\Omega ,L=1\cdot 5H,C=45\mu F$
2. $R=25\Omega ,L=1.5H,C=35\mu F$
3. $R=25\Omega ,L=2.5H,C=45\mu F$
4. $R=15\Omega ,L=3.5H,C=30\mu F$

Q. A LC circuit contains a $0.60\text{H}$ inductor and a $25\mu \text{F}$ capacitor. What is the rate of change of current (in ${\text{As}}^{-1}$) at the moment, when charge on the capacitor is $30\mu \text{C}$?

1. $2$
2. $3$
3. $4$
4. $6$
   

Q. The instantaneous values of current and emf in an ac circuit are $I=\frac{1}{\sqrt{2}}sin$ 314tamp and $E=\sqrt{2}sin(314t-\frac{\Pi }{6})$V respectively. The phase difference between E and I will be

1. -π / 6rad
2. -π / 3rad
3. π / 6rad
4. π / 3rad

Q. A telephone wire of length 200 km has a capacitance of $0.014\mu F$ per km. If it carries an ac of frequency 5 kHz, what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum

1. 0.35 mH
2. 35 mH
3. 3.5 mH
4. Zero

Q. In a series LCR circit R = 10 $\Omega$ and the impedance Z = 20 $\Omega$ . Then the phase difference between the current and the voltage is

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$

Q. In the circuit shown below, the key $K$ is closed at $t=0$. The current through the battery is

1. $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
2. $\frac{V(R_1+R_2)}{\sqrt{R_1^2+R_2^2}}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
3. $\frac{V}{R_2}$ at $t=0$ and $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=\infty$
4. $\frac{V}{R_1}$ at $t=0$ and $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=\infty$

Q.

Which one of the following curves represents the variation of impedance (Z) with frequency f in series LCR circuit

1. 
   

2. 
   

3. 
   

4. 
   

Q. In the circuit shown below what will be the reading of the voltmeter and ammeter respectively?

1. 200V, 1A
2. 800V, 2A
3. 100V, 2A
4. 220V, 2.2A

Q. The phase angle between e.m.f. and current in LCR series ac circuit is

1. $0to\frac{\pi }{2}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$
4. $\pi$

Q. In an LCR circuit, the potential difference between the terminals of the inductance is 60V, between the terminals of the capacitor is 30V and that across the resistance is 40V. Then, supply voltage will be:

1. 50V
2. 130V
3. 10V
4. 70V

Q. In series $\text{LR}$ circuit, $X_L=3R$. Now a capacitor with $X_C=R$ is added in series. Ratio of new to old power factor is

1. $1$
2. $2$
3. $\frac{1}{\sqrt{2}}$
4. $\sqrt{2}$

Q.

A circular coil of $16$ turns and radius $10\text{cm}$ carrying a current of $0.75A$ rests with its plane normal to an external field of magnitude $5.0\times {10}^{-2}T$. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of $2.0s^{-1}$ . What is the moment of inertia of the coil about its axis of rotation?

Q. In an RLC series circuit shown in the figure, the readinf of voltmeter $V_1$ and $V_2$ are $100V$ and $120V$, respectively. The source voltage is $130V$. For this situation, mark out the correct statement(s).

1. Voltage across resistor, inductor and capacitor are $50V$, $50\sqrt{3}V$ and $120+50\sqrt{3}V$ respectively
2. Voltage across resistor, inductor and capacitor are $50V$, $50\sqrt{3}V$ and $120-50\sqrt{3}V$ respectively
3. Pwer factor of the circuit is $5/13$
4. The circuit is capacitive in nature

Q. A $15\mu \text{F}$ capacitor is connected to $(220\text{V}$, $50\text{Hz})$ source. The RMS value of current in the circuit is nearly -

1. $1.52\text{A}$
2. $1.04\text{A}$
3. $0.92\text{A}$
4. $1.72\text{A}$

Q. Which of the following statements is incorrect about quality factor (Q) of a circuit (L-C-R in series)?

1. It is a dimensionless term
2. Large R indicates high quality factor
3. Ratio of inductive reactance to resistance at resonance frequency
4. It is directly proportional to band width

Q. In a series $\text{LCR}$ circuit $L=1\text{H},C=6.25\mu \text{F}$ and $R=1\Omega$. Its quality factor is-

1. $400$
2. $200$
3. $25$
4. $125$

Q. A choke coil is needed to operate an arc lamp at $250\text{V}$(rms) and $50\text{H}z$. The lamp has an effective resistance of $15\Omega$ when running at $10\text{A}$ (rms). The inductance of the choke coil is $\frac{N}{125\pi }\text{H}$. Find the value of $N$.

Q. In series R-L-C AC circuit,

1. Current is always behind inductor voltage
2. Current is always behind source voltage
3. Voltage across resistance is always a head of source voltage
4. Voltage across capacitor is always behind current

Q. The reading of A . C ammeter and voltage across capacitor in the given circuit are

1. 2 amp, $20V$
2. $4$ amp, $40V$
3. $3$ amp, $30V$
4. $5$ amp, $50V$

Q. A series RLC circuit has a bandwidth of $300\text{rad/s}$ at a resonance frequency of $3000\text{rad/s}$ when excited by a voltage source of $100\text{V}$. The inductance of the coil is $0.1\text{H}$. The quality factor is -

1. $10$
2. $20$
3. $30$
4. $40$

Q. There are two current carrying planar coils made each from identical wires of length L. $C_1$ is circular (radius R) and $C_2$ is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform $\underset{B}{\to }$ and carry the same current. Find a in terms of R.

Q. A certain series resonant circuit has a bandwidth of $2\text{kHz}$. If the existing coil is replaced with one having a higher value of $Q$ factor, the bandwidth will

1. Increase
2. Decrease
3. Remain the same
4. Be less selective

Q. Threshold frequency for different materials -

1. are same.
2. are different.
3. depend on incident light.
4. None of these

Q. A resonance circuit having inductance and resistance $2\times {10}^{-4}\text{H}$ and $6.28\Omega$ respectively oscillates at $10\text{MHz}$ frequency. The value of quality factor of this resonator is $[\pi =3.14]$

Q. An inductor of inductance $L=5\text{H}$ is connected to an $\text{AC}$ source having voltage $E=10\sin (10t+\frac{\pi }{6})$. Find the maximum value of current in the circuit.

1. $0.2\text{A}$
2. $2.5\text{A}$
3. $50\text{A}$
4. $1\text{A}$

Q. A coil of inductance $5\text{mH}$ and negligible resistance is connected to an oscillator giving an output voltage $E=10\sin \omega t$. The peak currents in the circuit for $\omega =10{\text{s}}^{-1},$$100{\text{s}}^{-1}$ and $500{\text{s}}^{-1}$ are $I_1,I_2$ and $I_3$ respectively. Then the ratio $I_1:I_2:I_3$ is:

1. $50:5:1$
2. $1:5:50$
3. $5:1:50$
4. $1:1:1$

Q. An inductance L, capacitance C and resistance R are connected in series across an AC source of angular frequency $\omega$. If ${\omega }^2>\frac{1}{LC}$ then :

1. emf leads the current
2. both the emf and the current are in phase
3. current leads the emf
4. emf lags behind the current

Q. An inductor of inductance, $L=5\text{H}$ is connected to an AC source having voltage, $V=10\sin (10t+\frac{\pi }{6})$. Find the inductive reactance.

1. $20\Omega$
2. $30\Omega$
3. $50\Omega$
4. $70\Omega$

Q. A capacitor of capacitive reactance $5\Omega$ is connected with $\text{AC}$ source having voltage $V=3\sin (\omega t+\frac{\pi }{6})$. Then

1. $I_{rms}=\frac{3}{\sqrt{2}}\text{A}$
2. $I_{rms}=\frac{3}{5\sqrt{2}}\text{A}$
3. Instantaneous current in the circuit is $\frac{3}{5}\sin (\omega t+\frac{2\pi }{3})$
4. Instantaneous current in the circuit is $\frac{3}{5\sqrt{2}}\sin (\omega t+\frac{2\pi }{3})$

Q. In the circuit shown in Figure, switch $S$ is closed at time $t=0$. Let $I_1$ and $I_2$ be the currents at any finite time $t$, then the ratio $I_1/I_2$

1. first increases, then decreases
2. is constant
3. increases with time
4. decreases with time