Impedance

Q.

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value

1. The resonance frequency will increase

2. The quality factor will increase

3. The quality factor and the resonance frequency will remain constant

4. The bandwidth of the resonance circuit will increase

Q. An ac voltage source $V=V_0\sin \omega t$ is connected across resistance $R$ and capacitance $C$ as shown in figure. It is given that $R=\frac{1}{\omega C}$. The peak current is $I_0$. If the angular frequency of the voltage source is changed to $\frac{\omega }{\sqrt{3}}$ by keeping $R$ and $C$ fixed, then the new peak current in the circuit is-

1. $\frac{I_0}{2}$
2. $\frac{I_0}{\sqrt{2}}$
3. $\frac{I_0}{\sqrt{3}}$
4. $\frac{I_0}{3}$

Q. When a $100\text{V DC}$ is applied across a solenoid, a current of 1.0 A flows in it. When a $100\text{V AC}$ is applied across the same coil, the current drops to $0.5\text{A}$. If the frequency of the $AC$ source is $50\text{Hz}$, the impedance and inductance of the solenoid are

1. $200\Omega$ and $0.55H$
2. $200\Omega$ and $1.0H$
3. $100\Omega$ and $0.86H$
4. $100\Omega$ and $0.93H$

Q. For a series $LCR$ circuit with $R=100\Omega$, $L=0.5\text{mH}$ and $C=0.1\text{pF}$ connected across $220\text{V}-50\text{Hz AC}$ supply, the phase angle between current and supplied voltage and the nature of the circuit is :

1. $\approx {90}^{\circ }$ , predominantly capacitive circuit
2. $\approx {90}^{\circ }$, predominantly inductive circuit
3. $0^{\circ }$ , resonance circuit
4. $0^{\circ }$, resistive circuit

Q.

A diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250pF$ in parallel with a load resistance $100$ kilo ohm. Find the maximum modulated frequency which could be detected by it.

Q. Assertion $\left(A\right)$: In series $\text{LCR}$ resonance circuit, the impedance is equal to the ohmic resistance.

Reason $\left(R\right)$: At resonance, the inductive reactance is equal and opposite to the capacitive reactance.

1. Both $\left(A\right)$ and $\left(R\right)$ are true, and $\left(R\right)$ is the correct explanation of $\left(A\right)$
2. Both $\left(A\right)$ and $\left(R\right)$ are true, and $\left(R\right)$ is not the correct explanation of $\left(A\right)$
3. $\left(A\right)$ is true but $\left(R\right)$ is false
4. $\left(A\right)$ is false but $\left(R\right)$ is true

Q.

Why $3^{rd}$ harmonic is dangerous?

Q. The percentage increase in the impedance of an a.c circuit, when its power factor changes form $0.866$ to $0.5$ is (if resistance of the circuit remains constant)

1. $73.2\%$
2. $86.6\%$
3. $90.8\%$
4. $66.6\%$

Q. a solenoiod of 10 henry induc†an ce and 2 ohm resis†an ce, is connected to a 10 volt battery.in how much time the magnetic energy will be reaches to 1/4th of the maximum value a)3.5sec b)2.5sec c)5.5sec d)7.5se

Q. In an $LR$ circuit, the value of $L$ is $\frac{0.4}{\pi }\text{H}$ and the value $R$ is $30\Omega$. If in the circuit, an alternating $emf$ of $200\text{V}$ $rms$ value at $50\text{cycles/s}$ is connected, the peak current of the circuit is $k\sqrt{2}\text{A}$ .The value of $k$ is (integer only)

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Q. A $15$ $\Omega$ resistor, an $80\text{mH}$ inductor and a capacitor of capacitance $C$ are connected in series with a $50\text{Hz}$ ac source. If the source voltage and current in the circuit are in phase, then the value of capacitance is

Q. $\text{Assertion}$:
When a variable frequency $AC$ source is connected to a capacitor, displacement current increases with increases in frequency.

$\text{Reason}$:
As frequency increases, conduction current also increases.

1. Both $\text{Assertion}$ and $\text{Reason}$ are correct, and $\text{Reason}$ is the correct explanation for $\text{Assertion}$
2. Both $\text{Assertion}$ and $\text{Reason}$ are correct, but $\text{Reason}$ is not the correct explanation for $\text{Assertion}$
3. $\text{Assertion}$ is correct, but $\text{Reason}$ is incorrect
4. Both $\text{Assertion}$ and $\text{Reason}$ are incorrect

Q. An alternating current of frequency 'f' is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit is

1. $R+2\pi fL$
2. $\sqrt{R^2+L^2}$
3. $\sqrt{R^2+2\pi fL}$
4. $\sqrt{R^2+4{\pi }^2{f}^2{L}^2}$

Q. In a series $\text{LCR}$ circuit, $C={10}^{-11}\text{F},L={10}^{-5}\text{H}$ and $R=100\Omega$. When a constant $\text{DC}$ voltage $E$ is applied to the circuit, the capacitor acquires a charge of ${10}^{-9}\text{C}$. The $\text{DC}$ source is replaced by a sinusoidal voltage source in which the peak voltage is $E$. At resonance, the peak value of the charge acquired by the capacitor is ${10}^{-n}\text{C}$. The value of $n$ is :

Q. Identify the graph which correctly represents the variation of capacitive resistance $X_C$ with frequency.

1. 
2. 
3. 
4. 

Q. A capacitor of $10\mu F$ and an inductor of $1H$ are joined in series. An $AC$ of $50\text{Hz}$ is applied to this combination. What is the impedance of the combination?

1. $\frac{5({\pi }^2-5)}{\pi }\Omega$
2. $\frac{100(10-{\pi }^2)}{\pi }\Omega$
3. $\frac{10({\pi }^2-5)}{\pi }\Omega$
4. $\frac{10(10-{\pi }^2)}{\pi }\Omega$

Q. 11. A sinusoidal supply of frequenoy 10 Hz and rmsvoltage 12 V is connected to a 2.1 uF capactorWhat is r.m.s. value of current?(1) 5.5 mA(2) 20 mA(3) 26 mA(4) 1.6 mA

Q. 47.A self inductance coil has a resistance of 31.4ohm and a self inductance of 17mH the frequency of AC at which the impedance is double of the resistance is 1)5000Hz. 2)500Hz 3)50Hz. 4)250Hz

Q. Consider an $LRC$ circuit as shown in figure, with an $\text{AC}$ source of peak value $V_0$ and angular frequency $\omega$. Then, the peak value of current through the $\text{AC}$ source is

1. $\frac{V_0}{\sqrt{\frac{1}{R^2}+{(\omega L-\frac{1}{\omega C})}^2}}$
2. $V_0{[\frac{1}{R^2}+{(\omega C-\frac{1}{\omega L})}^2]}^{1/2}$
3. $\frac{V_0}{\sqrt{R^2+{(\omega L-\frac{1}{\omega C})}^2}}$
4. None of these

Q. An AC supply with constant peak voltage and variable frequency is applied across a capacitor of capacitance $C$. Which of the following graphs correctly depicts the variation of peak current $\left(i\right)$ with angular frequency $\left(\omega \right)$?

1. 
2. 
3. 
4. 

Q. A capacitor of capacitance $12\mu \text{F}$ is joined to an $AC$ source of frequency $200\text{Hz}$. The $rms$ current in the circuit is $2\text{A}$. The $rms$ voltage across the capacitor is

1. $66.3\text{V}$
2. $132.6\text{V}$
3. $94\text{V}$
4. $47\text{V}$

Q. Let an $AC$ circuit contains a capacitor of capacitance $C=100\mu \text{F}$ only. If the instantaneous current in the circuit is $i=1.57\sin 100\pi t$. The expression for the instantaneous voltage, $E$ at this instantacross the capacitor will be

1. $E=50\sin (100\pi t-\frac{\pi }{2})$
2. $E=100\sin 50\pi t$
3. $E=50\sin 50\pi t$
4. $E=50\sin (100\pi t+\frac{\pi }{2})$

Q.

For an RLC circuit driven with a voltage of amplitude $v_m$ and frequency ${\omega }_0=\frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by

1. $\frac{R}{{\omega }_{0}C}$

2. $\frac{CR}{{\omega }_0}$

3. $\frac{{\omega }_{0}L}{R}$

4. $\frac{{\omega }_{0}R}{L}$

Q. Some AC circuits are given below, $i$ and $V$ are current and voltage of circuit.
Match the following.
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1. Option c missing
2. A(Q, S, T); B(R, S, T); C(P, T), D(Q, S, T)
3. Option d missing
4. Option b missing

Q.

How does the strength of the magnetic field produced by the current carrying solenoid vary with the number of turns in the coil ?

Q. Potential differences across resistor, inductor and capacitor are 60 V, 80 V and 20 V and all components in series. Then,

1. Current leads voltage by ${45}^{\circ }$
2. Voltage leads current by ${37}^{\circ }$
3. Power factor is $\sqrt{2}$
4. Voltage leads current by ${45}^{\circ }$

Q. A solenoid with inductance $L=7\text{mH}$ and active resistance $R=44\Omega$ is first connected to a source of direct voltage $V_0$ and then to a source of sinusoidal voltage with effective value $V=V_0$. At what frequency (in $\text{kHz}$) of the oscillator will the power consumed by the solenoid be $\eta =5$ times less than in the former case?

Q. The band width (in hertz) of an L, C, R series resonant circuit having resistance pi ohm, inductance 5 mH and capacitance of 20 μF is Options: a)20000 b)100 c)15000 d)5000

Q. When 100 volts dc is supplied across a solenoid, a current of 1.0 amperes flows in it. When 100 volts ac is applied across the same coil, the current drops to 0.5 ampere. If the frequency of ac source is 50 Hz, then the impedance and inductance of the solenoid are

1. $200\Omega and0.55henry$
2. $100\Omega and0.86henry$
3. $200\Omega and1.0henry$
4. $100\Omega and0.93henry$

Q. An electric bulb having small resistance and a capacitor are joined in series with an AC source whose frequency can be varied. On increasing the frequency of AC source, the glow of the bulb

1. increases.
2. decreases.
3. remains unchanged.
4. The bulb will not glow at all.