Inductor

Q.
In the figure, given that $V_{BB}$ supply can vary from $0\text{to}5.0\text{V}$, $V_{CC}=5\text{V},{\beta }_{dc}=200$, $R_B=100\text{k}\Omega ,R_C=1\text{k}\Omega$ and $V_{BE}=1.0\text{V}$. The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively:

1. $20\mu \text{A and 3.5 V}$
2. $20\mu \text{A and 2.8 V}$
3. $25\mu \text{A and 3.5 V}$
4. $25\mu \text{A and 2.8 V}$

Q. The transfer characteristic curve of a transistor, having input and output resistances $100\Omega$ and $100\text{k}\Omega$ respectively, is shown in the figure. The voltage gain is

1. $1\times {10}^4$
2. $5\times {10}^4$
3. $3\times {10}^4$
4. $4\times {10}^4$

Q. A $40\text{mH}$ inductor is connected to a $200\text{V},50\text{Hz}$ ac supply. The rms value of the current in the circuit is, nearly

1. $2.05\text{A}$
2. $16\text{A}$
3. $25.1\text{A}$
4. $1.7\text{A}$

Q. A pure inductor of $26\text{mH}$ is connected to an ac source of $220\text{V}$. Given frequency of the source as $50\text{Hz}$, the rms current in the circuit is

​​​​​​​$[$1 Mark$]$

1. $7\text{A}$
2. $14\text{A}$
3. $28\text{A}$
4. $742\text{A}$

Q. Match List-I with List-II :

	List–I		List–II
$\left(a\right)$	$\omega L>\frac{1}{\omega C}$	$\left(i\right)$	Current is in same phase with emf.
$\left(b\right)$	$\omega L=\frac{1}{\omega C}$	$\left(ii\right)$	Current lags behind the applied emf.
$\left(c\right)$	$\omega L<\frac{1}{\omega C}$	$\left(iii\right)$	Maximum current occurs.
$\left(d\right)$	Resonant frequency	$\left(iv\right)$	Current leads the emf.

Choose the correct answer from the options given below :

1. $\left(a\right)–\left(ii\right);\left(b\right)–\left(i\right);\left(c\right)-\left(iv\right);\left(d\right)–\left(iii\right)$
2. $\left(a\right)–\left(iii\right);\left(b\right)–\left(i\right);\left(c\right)-\left(iv\right);\left(d\right)–\left(ii\right)$
3. $\left(a\right)–\left(ii\right);\left(b\right)–\left(i\right);\left(c\right)-\left(iii\right);\left(d\right)–\left(iv\right)$
4. $\left(a\right)–\left(iv\right);\left(b\right)–\left(iii\right);\left(c\right)-\left(ii\right);\left(d\right)–\left(i\right)$

Q. Four different circuit components are given in column I-and all the components are connected across an AC source of same angular frequency $\omega =200\text{rad/s}$.
The information of phase difference between the current and source voltage in such situation of column -I is given in column-II.
Match the circuit components in column-I with corresponding result in column-II.

Which of the following options is the correct match?

1. $\left(A\right)\to q,r\left(B\right)\to p,t\left(C\right)\to p,r\left(D\right)\to q,t$
2. $\left(A\right)\to p,r\left(B\right)\to p,t\left(C\right)\to p,r\left(D\right)\to q,t$
3. $\left(A\right)\to q,r\left(B\right)\to q,t\left(C\right)\to q,r\left(D\right)\to q,t$
4. $\left(A\right)\to p,r\left(B\right)\to q,t\left(C\right)\to p,r\left(D\right)\to p,t$

Q. An inductor $(L=200\text{mH})$ is connected to an AC source of peak emf $210\text{V}$ and frequency $50\text{Hz}$. The value of peak current and instantaneous voltage of the source when the current is at its peak value is respectively :

1. $3.3\text{A},210\text{V}$
2. $6.6\text{A},0\text{V}$
3. $3.3\text{A},0\text{V}$
4. $6.6\text{A},210\text{V}$

Q. A $1\Omega$ voltmeter has a range of $1\text{V}$. Find the additional resistance which has to be joined in series with this voltmeter, to increase the range of the voltmeter to $100\text{V}$.

1. $10\Omega$
2. $\frac{1}{99}\Omega$
3. $99\Omega$
4. $100\Omega$

Q. A 200 V, 100 Watt bulb is to be used across an A.C source of peak voltage 400 V and an angular frequency of ${10}^3$ rad/s. The inductance of a choke coil to be used in series with the bulb so that the bulb won't blow off is

Q. In the following series $LCR$ circuit, find the peak value of source current $i_0$, voltage across capacitor $V_C$ and voltage across inductor $V_L$ at resonance, respectively.

1. $5\text{A},100\text{V},100\text{V}$
2. $2\text{A},100\text{V},200\text{V}$
3. $10\text{A},20\text{V},30\text{V}$
4. $5\text{A},50\text{V},50\text{V}$

Q. An ideal choke takes a current of $10\text{A}$ when connected to an ac supply of $125\text{V}$ and $50\text{Hz}$. A pure resistor under the same conditions takes a current of $12.5\text{A}$. If the two are connected to an $\text{AC}$ supply of $100\text{V}$ and $40\text{Hz}$, then the current in a series combination of the above resistor and inductor is

1. $5\sqrt{2}A$
2. $12.5A$
3. $20A$
4. $10A$

Q. The figure represents the voltage applied across a pure inductor. The diagram which correctly represents the variation of current $i$ with time $t$ is given by

1. 
2. 
3. 
4. 

Q. Given below are two statements.

Assertion - Resonance frequency will decrease in a series LCR circuit if a dielectric slab is inserted in between the plates of the capacitor.

Reason - By doing so, capacity of capacitor will increase.

Based on the above statements, choose the correct alternative.

1. Both assertion and reason are true, and reason is a correct explanation of assertion.
2. Both assertion and reason are true, but reason is not a correct explanation of assertion.
3. Assertion is true, but reason is false.
4. Assertion is false, but reason is true.

Q. A coil has negligible resistance and an inductive reactance of $20\Omega$ at $50\text{Hz}$. If an AC source of $200\text{V}$ and $100\text{Hz}$ frequency is connected across the coil, the rms current in the coil will be

1. $2.0\text{A}$
2. $5.0\text{A}$
3. $7.0\text{A}$
4. $10.0\text{A}$

Q. If the reading of voltmeter $V$ shown in the figure at resonance is $200\text{V}$, then the quality factor of the circuit is,

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

Q. An $AC$ circuit has $R=100\Omega ,C=2\mu F$ and $L=80\text{mH}$ connected in series. The quality factor of the circuit is :

1. $2$
2. $0.5$
3. $20$
4. $400$

Q. A $100W/200V$ bulb and an inductor are connected in series to a $220V/50Hz$ supply. Find the power consumed by the bulb.

1. $100W$
   
2. $92W$
   
3. $74W$
   
4. $84W$
   

Q. An arc lamp requires a direct current of $10\text{A}$ at $80\text{V}$ to function. If it is connected to a $220\text{V}\left(\text{rms}\right)$, $50\text{Hz}$ supply, the series inductor needed for it to work, is close to-

1. $80\text{H}$
2. $0.08\text{H}$
3. $0.044\text{H}$
4. $0.065\text{H}$

Q. An $\text{RLC}$ series circuit has $L=10\text{mH},R=3\Omega$ and $C=1\mu \text{F}$ connected in series to a source of $E=15\cos \omega t\text{V}$. If the frequency of the voltage is $10\%$ less than the resonant frequency, then

1. Peak value of current is $0.704\text{A}$
2. Impedance of the circuit is $21.32\Omega$
3. Power factor of the circuit is $0.141$
4. Resonant frequency of the circuit is $9\times {10}^3\text{rad/s}$

Q. As the frequency of an $AC$ circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?

1. Inductor and capacitor
2. Resistor and inductor
3. Resistor, inductor and capacitor
4. (a) and (c) above

Q. An inductor $L=20\text{mH}$, a resistor $R=100\Omega$ and a battery $E=10\text{V}$ are connected in series. After a long time the battery is short-circuited. Find the current in the circuit, $1\text{ms}$ after short-circuiting.
$[$Use $e^{-5}=0.00673]$

1. $6.7\times {10}^{-4}\text{A}$
2. $2.5\times {10}^{-4}\text{A}$
3. $0.5\times {10}^{-4}\text{A}$
4. $2\times {10}^{-3}\text{A}$

Q. An electric bulb, a capacitor, battery and a switch are all in series in a circuit. How does the intensity of light vary when the switch is turned on?

1. Continues to increase gradually
2. Gradually increases for some time and then becomes steady.
3. Sharply rises initially and then gradually decreases
4. Gradually increases for some then time and then gradually decreases

Q. A series $LCR$ circuit containing a resistor of resistance $120\Omega$ has resonant frequency $4\times {10}^5\text{rad/s}$. At resonance, the voltage across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively. Find the value of $C$.

1. $\frac{1}{2}\mu \text{F}$
2. $2\mu \text{F}$
3. $\frac{1}{9}\mu \text{F}$
4. $\frac{1}{32}\mu \text{F}$

Q. The angular frequency of alternating current in a $LCR$ circuit is $100\text{rad/s}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

1. $0.8\text{H}$ and $250\mu \text{F}$
2. $0.8\text{H}$ and $150\mu \text{F}$
3. $1.33\text{H}$ and $250\mu \text{F}$
4. $1.33\text{H}$ and $150\mu \text{F}$

Q. A series $LCR$ circuit is designed to resonate at an angular frequency ${\omega }_0=105\text{rad/s}$. The circuit draws $16\text{W}$ power from $120\text{V}$ source at resonance. The value of resistance $R$ in the circuit is $\Omega$

Q. The inductive reactance of a coil is $1000\Omega$. If its self inductance and frequency both are increased two times then inductive reactance will be

1. $1000\Omega$
2. $2000\Omega$
3. $4000\Omega$
4. $16000\Omega$

Q. An inductive circuit contains resistance of $1\Omega$ and an inductance of $2.0\text{H}$. If an $AC$ voltage of $120\text{V}$ and frequency $60\text{Hz}$ is applied to this circuit, the current would be nearly

1. $0.8\text{A}$
2. $0.48\text{A}$
3. $0.16\text{A}$
4. $0.32\text{A}$

Q. $e=10(1+0.8\cos 2000\pi t)\cos 3\times {10}^6\pi tvolt$. The depth of modulation is :

1. $8$
2. $0.8$
3. $800$
4. None of these

Q. An LCR circuit contains resistance of $110\Omega$ and a supply of $220\text{V}$ at $300\text{rad/s}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by ${45}^{\circ }$. If on the other hand, only inductor is removed the current leads by ${45}^{\circ }$ with the applied voltage. The rms current flowing in the circuit will be:

1. $2.5\text{A}$
2. $2\text{A}$
3. $1\text{A}$
4. $1.5\text{A}$

Q. A charged capacitor discharges through a resistance R with time constant $\tau$. The two are now placed in series across an AC source of angular frequency $\omega =\frac{1}{\tau }$ . The impedance of the circuit will be:

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