Resistors in Series and Parallel

Q. The current $\left(i_1\right)$ (in $A$) flowing through $1\Omega$ resistor in the following circuit is

1. $0.40A$
2. $0.20A$
3. $0.25A$
4. $0.5A$

Q. The figure shows a circuit having eight resistances of $1\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages ${\epsilon }_1=12\text{V}$ and ${\epsilon }_2=6\text{V}$.



Which of the following statement(s) is(are) correct?

1. The magnitude of current flowing through $R_1$ is $7.2\text{A}$.
2. The magnitude of current flowing through $R_4$ is $2.4\text{A}$
3. The magnitude of current flowing through $R_3$ is $4.8\text{A}$.
4. The magnitude of current flowing through $R_2$ is $1.2\text{A}$.

Q. 21.n a circuit a metallic wire is connected in series with a battery and an ammeter.if another wire(same metal, same length and cross sectional area )is connected in parallel to the metallic wire , the current in ammeter will be: A)halved B) doubled C)four times D) same

Q. 119.An ac voltage is applied to a resistance R and an inductor L in series. If R and inductive reactance are both equal to 3 ohm, the phase difference between the applied voltage and the current in the circuit is 1) pie/6 2) pie/4 3) pie/2 4) 0

Q. Two resistors, $4\Omega$ and $6\Omega$ are connected in parallel with a $6\text{V}$ battery of negligible resistance. Calculate the current flowing through $4\Omega$ resistor.

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

Q. Twelve resistors each of resistance $r$ are connected together so that each lies along the edge of the cube as shown in the figure. The equivalent resistance between points $1$ and $4$ is

1. $\frac{5r}{12}$
2. $\frac{7r}{12}$
3. $\frac{11r}{12}$
4. $\frac{13r}{12}$

Q. The depletion layer in a silicon diode is $1\mu \text{m}$ wide and the knee potential is $0.6\text{V}$, then the electric field in the depletion layer will be

1. Zero
2. $0.6{\text{Vm}}^{-1}$
3. $6\times {10}^4{\text{Vm}}^{-1}$
4. $6\times {10}^5{\text{Vm}}^{-1}$

Q. In the circuit shown in figure, emf of the batteries are $E_1=3\text{V},E_2=2\text{V},E_3=1\text{V}$ and their internal resistances are $R=r_1=r_2=r_3=1\Omega$. The potential difference between the points $\text{A}$ and $\text{B}$, and the current through branch containing resistor $r_2$ will be respectively

1. $2\text{V},1\text{A}$
2. $3\text{V},2\text{A}$
3. $2\text{V},0\text{A}$
4. $4\text{V},1.5\text{A}$

Q. In the figure shown, what is the current (in $\text{Ampere}$) drawn from the battery? You are given:
$R_1=15\Omega ,R_2=10\Omega ,R_3=20\Omega ,R_4=5\Omega ,R_5=25\Omega ,R_6=30\Omega ,E=15\text{V}$

1. $20/3$
2. $7/18$
3. $13/24$
4. $9/32$

Q. Consider the circuit shown in the figure

1. The current in the $5\Omega$ resistor is $2\text{A}$
2. The current in the $5\Omega$ resistor is $1\text{A}$
3. The potential difference $V_A-V_B$ is $10\text{V}$
4. The potential difference $V_A-V_B$ is $5\text{V}$

Q. Potential drop across $5\Omega$ is $10V$, then EMF of the battery is

1. $12\text{V}$
2. $28\text{V}$
3. $30\text{V}$
4. $40\text{V}$

Q. A resistor with resistance of $10\text{M}\Omega$ is connected in series with a capacitor of capacitance $1\mu \text{F}$ and a battery with e.m.f. $E=12\text{V}$. Before the switch is closed at time $t=0,$ the capacitor is uncharged. What fraction of the final charge is on the plates at time, $t=46\text{s}$? $(e^{-4.6}=0.01)$

1. $99\%$
   
2. $10\%$
3. $20\%$
   
4. $50\%$
   

Q. In the circuit shown in figure, $E_1$ and $E_2$ are two ideal sources of unknown emfs. Current flowing through resistor of resistance $R\Omega$ is $2A$ and through resistor of resistance $4\Omega$ is $3A$ as shown. If potential difference across $6\Omega$ resistance is $V_A-V_B=10\text{V}$, then the value of $(E_2-E_1)R$( in $V.\Omega$) is

Q. In the figure shown, the potential difference between points A and B is :

1. $10\text{V}$
2. $30\text{V}$
3. $7.5\text{V}$
4. None

Q. Several capacitors are connected as shown in the given figure. If the charge on the $5\mu \text{F}$ capacitor is $120\mu \text{C}$ , the potential between points $A$ and $D$ is

1. $24\text{V}$
2. $96\text{V}$
3. $16\text{V}$
4. $0\text{V}$

Q. A 100 W and 500 W bulb are joined in parallel with the mains . Which bulb will glow brighter?Give reasons

Q. $AB$ is a part of another large circuit. Also $V_Q-V_B=12V$ Then

1. Current, $i=3A$
2. Current $i=5A$
3. $V_A-V_B=12V$
4. $V_A-V_B=24V$

Q. In the circuit shown below, the current that flows from a to b when the switch S is closed is

1. + 1.0 A
2. + 1.5 A
3. - 1.0 A
4. - 1.5 A

Q. Eight identical resistances $r$ are connected as shown in figure. Find equivalent resistance between $A$ and $D$.

1. $\frac{7r}{16}$
2. $\frac{2r}{9}$
3. $\frac{8r}{15}$
4. $\frac{7r}{19}$

Q.

Find the charges on the four capacitors of capacitances 1$\mu F,2\mu F,3\mu F$ and $\mu F$ shown in figure (32 - E32). Figure 32 - E32

Figure 32 - E32

Q.

Find the current measured by the ammeter in the circuit shown in figure (32-E18)

Q. Two capacitors of capacitances $C_1$ and $C_2$ , in a circuit are joined as shown in the figure. The potential of point $\text{A}$ is $V_1$ and potential of point $\text{B}$ is $V_2$. The potential at point $\text{D}$ will be

1. $\frac{1}{2}(V_1+V_2)$
   
2. $\frac{(C_2{V}_1+C_1{V}_2)}{C_1+C_2}$
   
3. $\frac{(C_1{V}_1+C_2{V}_2)}{C_1+C_2}$
   
4. $\frac{2(C_1{V}_1+C_2{V}_2)}{C_1+C_2}$
   

Q. Three resistors having resistances, $r_1,r_2$ and $r_3$ are connected as shown in the given circuit. The ratio $\frac{i_3}{i_1}$ of currents in terms of resistances used in the circuit is -

1. $\frac{r_2}{r_1+r_3}$
2. $\frac{r_1}{r_2+r_3}$
3. $\frac{r_2}{r_2+r_3}$
4. $\frac{r_1}{r_1+r_2}$

Q. A potentiometer consists of a wire of length 200 cm and of resistance 5 ohm. It is connected to a cell of emf 1 V having negligible internal resistance. The potential difference per unit length of the wire, is (1) 1 V/m (2) 0.5 V/m (3) 2 V/m (4) 3 V/m

Q. In the circuit shown in the figure, a $12\text{volt}$ battery has been connected across the points $\text{X}$ and $\text{Y}$. The work done by battery will be:

1. 
   $180\mu \text{J}$
2. 
   $384\mu \text{J}$
3. 
   $424\mu \text{J}$
4. 
   $212\mu \text{J}$

Q. (a) Three resistors 1 W, 2 W, and 3 W are combined in series. Whatis the total resistance of the combination? (b) If the combination is connected to a battery of emf 12 V andnegligible internal resistance, obtain the potential drop acrosseach resistor.

Q. A current of $2\text{ampere}$ flows in a system of conductors as shown in the following figure. The potential difference $(V_A-V_B)$ will be (in $\text{volts}$):

1. $+2$
2. $-1$
3. $+1$
4. $-2$

Q. Consider an infinite mesh as shown in figure. Each side of the mesh has resistance $R$. Consider the hexagonal part ABCDEF of the infinite mesh. Equivalent resistance between any two points of the hexagon is measured. Equivalent resistance between A and B is $\frac{\alpha R}{\beta }$. Find the least value of $\alpha +\beta$.

Q. In the following figure, the potential difference is shown on $R,L$ & $C$. The emf of source in $\text{volt}$ is

1. $190$
2. $70$
3. $50$
4. $40$

Q. Potential drop across $5\Omega$ is $10V$, then EMF of the battery is

1. $12\text{V}$
2. $28\text{V}$
3. $30\text{V}$
4. $40\text{V}$