Parallel Combination of Cells

Q.

Derive an expression for three resistances connected in parallel.

Q. A hollow charged metal sphere has radius $r$. If the potential difference between its surface and a point at a distance $3r$ from the centre is $V$, then electric field intensity at distance $3r$ from the centre is

1. $\frac{V}{3r}$
2. $\frac{V}{4r}$
3. $\frac{V}{2r}$
4. $\frac{V}{6r}$

Q. Five identical cells each of internal resistance $1\Omega$ and emf $5\text{V}$ are connected in series and in parallel with an external resistance '$R$'. For what value of '$R$', current in series and parallel combination will remain the same?

1. $10\Omega$
2. $1\Omega$
3. $5\Omega$
4. $25\Omega$

Q. The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2\Omega$. The value of internal resistance of each cell is

1. $4\Omega$
2. $2\Omega$
3. $8\Omega$
4. $6\Omega$

Q. When the two identical cells are connected either in series or in parallel across a 4 ohm resistor they send the same current through it. The internal resistance of the cell is

1. $4\Omega$
2. $4.8\Omega$
3. $2\Omega$
4. $1.2\Omega$

Q.

Draw a schematic diagram of a circuit consisting of a battery of $3\mathrm{cells}$ of $2\mathrm{V}$ each, a combination of three resistors of $10\mathrm{\Omega },20\mathrm{\Omega }$, and connected in parallel, a plug key, and an ammeter, all connected in series. Use this circuit to find the value of the current through each resistor.

Q. In a common-base configuration of transistor$\alpha =0.98,I_B=0.02\text{mA},R_L=5\text{k}\Omega$.
Output voltage across load is (approximately)

1. $6.2\text{V}$
2. $3.2\text{V}$
3. $5.2\text{V}$
4. $4.9\text{V}$

Q. Find the potential difference between the points P and Q in the given circuit?

1. 3V
2. 3.75V
3. 3.25V
4. 3.5V

Q. Quality factor of the given circuit is

1. 2
2. 1
3. 0.8
4. 0.4

Q. In the given circuit the reading of ideal voltmeter is $E/2$. The internal resistance of the battery is

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

Q. Three concentric spherical conductors are arranged as shown in the figure. The potential at point $\text{P}$ will be:

1. $\frac{1}{4\pi {ϵ}_0}[\frac{Q_1}{r}+\frac{Q_2}{r}+\frac{Q_3}{r}]$
2. $\frac{1}{4\pi {ϵ}_0}[\frac{Q_1+Q_2}{r}+\frac{Q_3}{c}]$
3. $\frac{1}{4\pi {ϵ}_0}[\frac{Q_1}{a}+\frac{Q_2}{b}+\frac{Q_3}{c}]$
4. $\frac{1}{4\pi {ϵ}_{0}c}\times [Q_1+Q_2+Q_3]$

Q. In a purely resistive AC circuit, which of the following graphs, best represents the variation of the magnitude of peak current $\left(I_o\right)$ with the angular frequency $\left(\omega \right)$ of the AC supply?

1. 
2. 
3. 
4. 

Q. In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?

1. Only a capacitor
2. Resistor and capacitor
3. Only resistor
4. Resistor and an inductor

Q. Find the value of resistor to be connected between $\text{C}$ and $\text{D}$, so that the resistance of the entire circuit between $\text{A}$ and $\text{B}$ does not change with the number of elementary sets.

1. $R$
2. $R(\sqrt{3}-1)$
   
3. $3R$
4. $R(\sqrt{3}+1)$
   

Q.

A single battery fo emf E and internal resistance r is equivalent to a parallel combination of two batteries of emfs $E_1=2V$ and $E_2=1.5V$ and internal resistances $r_1=1\Omega$ and $r_2=2\Omega$ respectively, with polarities as shown in the figure.

(IIT-JEE 1997)

1. $E=\frac{5}{6}V$

2. r = 1.5 Ω

3. E = 1.2 V

4. $r=\frac{2}{3}\Omega$

Q. Find the current through $2\text{V}$ battery.

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

Q.
In the figure shown, the current in the $10\text{V}$ battery is close to :

1. $0.71\text{A}$ from positive to negative terminal
2. $0.42\text{A}$ from positive to negative terminal
3. $0.21\text{A}$ from positive to negative terminal
4. $0.36\text{A}$ from negative to positive terminal

Q.

Six identical cells each of $e.m.f.2V$ and internal resistance $0.2\mathrm{\Omega }$ are connected in parallel to form a battery. An external resistance of $5\mathrm{\Omega }$ is connected to this battery. Draw the circuit diagram of the above arrangement. What is the current in $5\mathrm{\Omega }$ resistor.

Q. The potential difference between the points P and Q in the given circuit is .

1. 0.44V
2. 1.55V
3. 2.66V
4. 1.33V

Q. Find the current through R₃ in the circuit as shown in figure?

1. 2A
2. 3A
3. 3.5A
4. 2.5A

Q. Five conducting parallel plates having area $A$ and separation between them $d$ are placed as shown in figure. Plate number $2$ and $4$ are connected and between points $\text{A}$ and $\text{B}$ a cell of emf $E$ is connected. The charge flow through the cell is

1. $\frac{2}{3}\frac{{ϵ}_{0}AE}{d}$
2. $\frac{{ϵ}_{0}AE}{d}$
3. $\frac{4{ϵ}_{0}AE}{d}$
4. $\frac{3}{4}\frac{{ϵ}_{0}AE}{d}$

Q. Three voltmeters are connected as shown.


A potential difference has been applied across $A$ and $B$. On closing the switch $S$, what will be the effect on the readings of voltmeters ?

1. $V_1$ increases
2. $V_2$ decreases
3. $V_2$ and $V_3$ both increase
4. One of $V_2$ and $V_3$ increases and the other decreases

Q. Find the current through the resistor B in the given circuit. Each resistor has a resistance of $10\Omega$ and each battery has an EMF of 10 V.

1. 0A
2. 10A
3. 0.1A
4. 1A

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

1. $R=25\Omega ,L=2.5H,C=45\mu F$
   
2. $R=15\Omega ,L=3.5H,C=30\mu F$
3. $R=25\Omega ,L=1.5H,C=45\mu F$
4. $R=20\Omega ,L=1.5H,C=35\mu F$

Q. A number of capacitors, each of equal capacitance $C$, are arranged as shown in the figure. The equivalent capacitance between A and B is

1. $(2n+1)C$
2. $n^{2}C$
3. $\frac{(n-1)n}{2}C$
4. $\frac{(n+1)n}{2}C$

Q. Two resistors of resistances $R_1$ = (300 $\pm$ 3) $\Omega$ and $R_2$ = (500 $\pm$ 4) $\Omega$ are connected in series. The equivalent resistance of the series combination is

1. (800 $\pm$ 1) $\Omega$
2. (800 $\pm$ 7) $\Omega$
3. (200 $\pm$ 7) $\Omega$
4. (200 $\pm$ 1) $\Omega$

Q. A circuit is shown below.


Currently the switch is in position A and steady current is flowing through circuit. Capacitor is uncharged. At $t=0$, switch is instantly moved to position B.
Find the current in the $LC$ circuit.$\left(\mathrm{Given}\mathrm{that}\omega =\frac{1}{\sqrt{LC}}\right)$

1. $\frac{V}{R}\sin \left(\omega t\right)$
2. $\frac{V}{R}\cos \left(\omega t\right)$
3. $\frac{V}{R}\cos \left(\omega t+\frac{\pi }{5}\right)$
4. $\frac{V}{R}\cos \left(\omega t+\frac{\pi }{8}\right)$

Q. When the two identical cells are connected either in series or in parallel across a 4 ohm resistor they send the same current through it. The internal resistance of the cell is

1. $1.2\Omega$
2. $2\Omega$
3. $4\Omega$
4. $4.8\Omega$

Q. the cell delivers equal power to load resistances R1 and R2 individually the value of internal resistance of the cell is

Q. Two Resistor $2\Omega$ and $4\Omega$ are connected in parallel. Two more Resistor $3\Omega$ and $6\Omega$ are connected in parallel. These two combinations are in series with a battery of emf $5V$ and internal Resistance $0.7\Omega$. Calculate the current through $6\Omega$ Resistors.