Capacitive Reactance

Q. The frequency for which a 5 $\mu$ F capacitor has reactance of $\frac{1}{1000}\Omega$ is given by

1. $\frac{{10}^6}{\pi }Hz$
2. $\frac{{10}^8}{\pi }Hz$
3. $\frac{1}{1000}Hz$
4. $1000Hz$

Q. A bulb and a capacitor are in series with an ac source. On increasing frequency how will glow of the bulb change

1. The bulb quenches
2. The glow decreases
3. The glow increases
4. The glow remain the same

Q. An alternating voltage V = 200 sin 100t, where V is in volt and t seconds, is connected to a series combination of 1$\mu$ farad capacitor and 10K $\Omega$ resistor through an AC ammeter. The reading of the ammeter will be

1. $\sqrt{2}mA$
2. $10\sqrt{2}mA$
3. $2mA$
4. $10mA$

Q. An AC voltage source, $V=200\sqrt{2}\sin 100t$, is connected across a circuit containing an AC ammeter and capacitor of capacity $1\mu F$. Reading of the ammeter is:

1. $10\text{mA}$
2. $20\text{mA}$
3. $40\text{mA}$
4. $80\text{mA}$

Q. A bulb and a capacitor are in series with an ac source. On increasing frequency, glow of the bulb .

1. increases
2. decreases
3. remains same
4. quenches

Q.

An alternating voltage E =50 sin(100 t)V is connected to a 1 μF capacitor through an ac ammeter. What will be the reading of the ammeter?

1. 10 mA

2. 5 mA

3. 
   

4. 
   

Q. An alternating voltage $E=200\sqrt{2}sin\left(100t\right)$ is connected to a 1 microfarad capacitor through an ac ammeter. The reading of the ammeter shall be

1. 10 mA
2. 20 mA
3. 40 mA
4. 80 mA

Q.

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50Hz AC supply, the series inductor needed for it to work is close to:

1. 0.88 H

2. 0.44 H

3. 0.065 H

4. 80 H

Q.

How does the $RC$ circuit work?

Q. A wire having a linear mass density $5.0\times {10}^{-3}kg/m$ is stretched between two rigid supports with tension of $450N$. The wire reasonates at frequency $400Hz$. The next higher frequency at which the wire resonates is $500Hz$. The length of the wire will be

1. $1m$
2. $4m$
3. $4.5m$
4. $1.5m$

Q. The frequency for which a 5 $\mu$ F capacitor has reactance of $\frac{1}{1000}\Omega$ is given by

1. $\frac{{10}^6}{\pi }Hz$
2. $\frac{{10}^8}{\pi }Hz$
3. $\frac{1}{1000}Hz$
4. $1000Hz$

Q. A capacitor is a perfect insulator for

1. Both ac and dc
2. Direct currents
3. None of these
4. Alternating currents

Q. What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A	Voltage V	Current A	Voltage V
0.2	3.94	3.0	59.2
0.4	7.87	4.0	78.8
0.6	11.8	5.0	98.6
0.8	15.7	6.0	118.5
1.0	19.7	7.0	138.2
2.0	39.4	8.0	158.0

Q. A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by $45\%$ and tension is
increased by $21\%$. Now its fundamental frequency:

1. increases by $50\%$
2. increases by $100\%$
3. decreases by $50\%$
4. decreases by $25\%$

Q. The frequency for which a $5.0\mu F$ capacitor has a reactance of $1000\Omega$ is given by:

1. $\frac{1000}{\pi }$ cycles/sec
2. $\frac{100}{\pi }$ cycles/sec
3. $200$ cycle/s
4. $5000$ cycles/sec

Q. On radiating (sending out) an AM modulated signal, the total radiated power is due to energy carried by ${\omega }_c,{\omega }_c-{\omega }_m$ & ${\omega }_c+{\omega }_m$. Suggest ways to minimize cost of radiation without compromising on information.

Q. Two alternating voltage generators produce emfs of the same amplitude $E_0$ but with a phase difference of $\pi /3$. The resultant emf is:

1. $E_0\sin [\omega t+(\pi /6\left)\right]$
2. $E_0\sin [\omega t+(\pi /3\left)\right]$
3. $\sqrt{3}{E}_0\sin [\omega t+(\pi /6\left)\right]$
4. $\sqrt{3}{E}_0\sin [\omega t+(\pi /2\left)\right]$

Q. The tuning circuit of a radio receiver has a resistance of $50\Omega$, an inductor of $10mH$ and a variable capacitor. A $1MHz$ radio wave produces a potential difference of $0.1mV$. The value of the capacitor to produce resonance is (take ${\pi }^2$ $=10)$

1. $2.5pF$
2. $5.0pF$
3. $25pF$
4. $50pF$

Q. The frequency for which $5\mu F$ capacitor has a reactance of $10,000\Omega$ is

1. $\left(100/\pi \right)$ cycles per second
2. $\left(10/\pi \right)$ cycles per second
3. $200$ cycles per second
4. $5,000$ cycles per second

Q. A coil has an inductance of 0.7H and is joined in series with a resistance of 220 $\Omega$ . When an alternating e.m.f. of 220V at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is

1. 0.5 ampere
2. 5 ampere
3. 7 ampere
4. 0.7 ampere

Q. An unchanged capacitor is connected in circuit as shown in figure. Power ratings of bulbs are given in diagram. At $t=0$ switch is closed select correct alternatives :

1. At $t=0$ power consumption in circuit is $\frac{3P_0}{2}$
2. After a long time power consumption in circuit is $\frac{P_0}{2}$
3. Brightness of $B_1$ decreases with time.
4. Initially Brightness of bulb $B_2$ is less than brightness of $B_1$, but later on after certain time $B_2$ will be brighter.

Q. An electric bulb and a capacitor are connected in series with an $AC$ source. On increasing the frequency of the source, the brightness of the bulb:

1. increase
2. decreses
3. remains unchanged
4. sometime incenses and something decreases

Q. A bulb and a capacitor are in series with an ac source. On increasing frequency, glow of the bulb .

1. increases
2. decreases
3. remains same
4. quenches

Q. At a frequency ${\omega }_0$ the reactance of a certain capacitor equals that of a certain inductor. If frequency is changed to 2 ${\omega }_0$ . The ratio of reactance of the inductor to that of the capacitor is

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

Q. A resistor $R$ and $2\mu F$ capacitor in series is connected through a switch to $200$ $V$ direct supply. Across the capacitor is a neon bulb that lights up at $120$ $V$. Calculate the value of $R$ make the bulb light up $5$ $s$ after the switch has been closed $({\log }_{10}2.5=0.4).$

1. $1.3\times {10}^4\Omega$
2. $1.7\times {10}^6\Omega$
3. $2.7\times {10}^6\Omega$
4. $3.3\times {10}^7\Omega$

Q. An ac source of angular frequency $\omega$ is fed across a resistor r and a capacitor C in series. The current registered is I. If now the frequency of source is changed to $\frac{\omega }{4}$ (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$

1. $\sqrt{\frac{3}{5}}$
2. $\sqrt{\frac{2}{5}}$
3. $\sqrt{\frac{1}{5}}$
4. $\frac{1}{2}$

Q. The capacitive reactance of a condenser of capacity 25$\mu$F for an AC of frequency 4000 Hz will be

1. $\frac{5}{\pi }\Omega$
2. $\frac{10}{\pi }\Omega$
3. $5\pi \Omega$
4. $\frac{\pi }{5}\Omega$

Q. An inductance $L$, a capacitance $C$ and a resistance $R$ may be connected to an $AC$ source of angular frequency $\omega$, in three different combinations of $RC,RL$ and $LC$ in series. Assume that $\omega L=\frac{1}{\omega C}$. The power drawn by the three combinations are $P_1,P_2,P_3$ respectively. Then,

1. $P_1=P_2=P_3$
2. $P_1=P_2>P_3$
3. $P_1>P_2>P_3$
4. $P_1=P_2<P_3$

Q. In series $\text{CR}$ circuit excited by ac mains, $C=10\mu F,R=300\Omega$. Find the power factor.

1. $\frac{3}{\sqrt{16}}$
2. $\frac{3}{\sqrt{17}}$
3. $\frac{3}{\sqrt{18}}$
4. $\frac{3}{\sqrt{19}}$

Q. When the incident frequency is $f_0,K$ is the $(KE{)}_{max}$ of the electrons emitted and $\varphi$ is the work function of the surface. If incident frequency is doubled, new $(KE{)}_{max}$ will be

1. 2 $K-2\varphi$
2. 2 $K$
3. 2 $K+\varphi$
4. 2 $K-\varphi$