Power in Electric Circuits

Q. Three identical bulbs are connected as shown in figure. When switch $S$ is open, the power consumed in bulb $B$ is $P$. What will be the power consumed by the same bulb when switch $S$ is closed?

1. $\frac{9P}{4}$
2. $\frac{16P}{9}$
3. $\frac{9P}{16}$
4. $\frac{4P}{9}$

Q. A battery of internal resistance $4\Omega$ is connected to the network of resistances as shown in the figure. In order that the maximum power can be delivered to the network, the value of 𝑅 in $\Omega$ should be

1. $18$
2. $\frac{4}{9}$
3. $2$
4. $\frac{8}{3}$

Q. To get maximum current through a resistance of $2.5\Omega$, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5\Omega$. What are the values of $n$ and $m$ if the total number of cells is $45$?

1. $m=3,n=15$
2. $m=5,n=9$
3. $m=9,n=5$
4. $m=15,n=3$

Q. Two cells, each of e.m.f. $E$ and internal resistance $r$, are connected in parallel across a resistor $R$ as shown in the figure. The power dissipated through the resistor $R$ is maximum if :

1. $R=r$
2. $R=2r$
3. $R=\frac{3r}{2}$
   
4. $R=\frac{r}{2}$
   

Q. A heater is designed to operate with a power of $1000\text{W}$ in a $100\text{V}$ supply line. It is connected in combination with a resistance of $10\Omega$ and a resistance $R$ to a $100\text{V}$ power supply as shown in figure. What will be the value of $R$ , such that heater operates with a power of $62.5\text{W}$?

1. $7\Omega$
2. $5\Omega$
3. $10\Omega$
4. $14\Omega$

Q. Two resistors, $R_1$ and $R_2$ are connected in series. If the current through the resistor $R_1$ is $2\text{A}$ and the power dissipated in the resistor $R_2$ is $10\text{W},$ then the value of resistance of the resistor $R_2$ is

1. $3.9\Omega$
2. $1.9\Omega$
3. $4\Omega$
4. $2.5\Omega$

Q. A battery has an open circuit potential difference of $6\text{V}$ between its terminals. When a load resistance of $60\Omega$ is connected across the battery, the total power dissipated by the battery is $0.4\text{W}$. What should be the load resistance $R$, so that maximum power will be dissipated in $R$ ?

1. $20\Omega$
2. $30\Omega$
3. $40\Omega$
4. $60\Omega$

Q. In Circuit-1 and Circuit-2 shown in the figures, $R_1=1\Omega ,R_2=2\Omega \text{and}{R}_3=3\Omega$. $P_1\text{and}{P}_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1\text{and}{Q}_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1\text{and}{S}_2$ are in closed conditions, respectively.




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

1. When a constant current source of $2\text{Amp}$ is connected across $A$ and $B$ in both circuits, $Q_2<Q_1$.
2. When a constant current source of $2\text{Amp}$ is connected across $A$ and $B$ in both circuits. $P_1>P_2$.
3. When a voltage source of $6\text{V}$ is connected across $A$ and $B$ in Circuit-1, $Q_1>P_1$.
4. When a voltage source of $6\text{V}$ is connected across $A$ and $B$ in both circuits, $P_1<P_2$.

Q. The circuit shown below is working as a $8\text{V}$ DC, regulated voltage source. When $12\text{V}$ is used as input, the power dissipated $\text{in mW}$ in each diode is; (considering both Zener diodes are identical)_______.

Q. The relation between $R$ and $r$ for which the power consumed in the external part of the circuit is maximum.

1. $R=r$
2. $R=\frac{r}{2}$
3. $R=2r$
4. $R=1.5r$

Q. Two bulbs, one of $200\text{Volts},60\text{Watts}$ and the other of $200\text{Volts},100\text{Watts}$ are connected in series to a $200\text{Volt}$ supply. The power consumed will be

1. $37.5\text{Watt}$
2. $160\text{Watt}$
3. $62.5\text{Watt}$
4. $110\text{Watt}$

Q. A $25W-120V$ bulb and a $100W-120V$ bulb are connected in series across a $120V$ line. Which bulb will glow brighter?

1. $25W-120V$
2. $100W-120V$
3. both will have same incandescence
4. Neither will give any light

Q. The wattage rating of a light bulb indicates the power dissipated by the bulb if it is connected across $110\text{V}$ DC potential difference. If a $50\text{W}$ and $100\text{W}$ bulb are connected in series to a $110\text{V}$ DC source, how much power will be dissipated in the $50\text{W}$ bulb?

1. $50\text{W}$
2. $100\text{W}$
3. $22\text{W}$
4. $11\text{W}$

Q. Heater-$1$, takes $3$ minutes to boil a given amount of water. Heater-$2$ takes $6$ minutes. If $t_1$ and $t_2$ are the time taken to boil the same amount of water, when the two heaters are connected in series and parallel, respectively, then $\frac{t_1}{t_2}=?$

$[$Assume same cell is connected in all the cases$]$

1. $\frac{9}{2}$
2. $\frac{2}{9}$
3. $\frac{4}{9}$
4. $\frac{9}{4}$

Q. All bulbs consume same power. The resistance of bulb $1$ is $36\Omega$.


$\left(i\right)$ What is the resistance of bulb $3?$

1. $4\Omega$
2. $9\Omega$
3. $12\Omega$
4. $18\Omega$

Q. A heater is designed to operate with a power of $1000\text{W}$ in a $100\text{V}$ line. It is connected, in combination with a resistance $R$, to a $100\text{V}$ main supply as shown in Figure. What should be the value of $R$ such the heater may operate with a power of $62.5\text{W}$?

1. $50\Omega$
2. $25\Omega$
3. $15\Omega$
4. $5\Omega$

Q. Two bulbs $A$ and $B$ rated $40W$, $220V$ and $60W$, $220V$, respectively, are connected in series across a $220V$ supply. As a result:

1. $A$ and $B$ will burn with the same brightness
2. $A$ burns more brightly
3. $B$ burns more brightly
4. Both will be dim

Q. Find the value of $R$, such that maximum power is transfereed to it.

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

Q. Two bulbs $A$ and $B$ rated $25W$, $220V$ and $100W$, $220V$, respectively, are connected in series across a $440V$ mains. As a result:

1. $A$ will burn out.
2. $B$ will burn out.
3. Both $\left(1\right)$ and $\left(2\right)$ burn with same brightness.
4. Neither $\left(1\right)$ or $\left(2\right)$ will glow.

Q.
Given figure shows arrangement of six bulbs and two battries each bulb is rated at 100V and there power is shown in figure
List I gives bulbs and list II gives there output power

With $S_2$ closed and $S_1$ open.
$\begin{array}{cc}\text{List~I}& \text{List~II}\\ \text{I)}{B}_1& \text{P)}\frac{256}{9}\\ \text{II)}{B}_2& \text{Q)}\frac{128}{9}\\ \text{III)}{B}_3& \text{R)}\frac{200}{9}\\ \text{IV)}{B}_4& \text{S)}\frac{512}{9}\\ & \text{T)}\frac{800}{9}\\ & \text{U)}\frac{400}{9}\end{array}$

1. $I\to P,II-R,III\to S,IV-Q$
2. $I\to P,II\to S,III\to P,IV\to Q$
3. $I-Q,II-T,III-P,IV-U$
4. $I-Q,II\to T,III\to U,IV\to R$

Q. The power dissipated by $R=2\Omega$ resistor is -

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

Q. A cell of internal resistances $r$ is connected to a load of resistance $R$. Energy is dissipated in the load, but some thermal energy is also wasted in the cell. The efficiency of such arrangement is found from the expression

$\frac{\text{Energy dissipated in the load}}{\text{Energy dissipated in the complete circuit}}$

Which of the following gives the efficiency in this case?

1. $\frac{r}{R}$
2. $\frac{R}{r}$
3. $\frac{r}{R+r}$
4. $\frac{R}{R+r}$

Q. The voltage across the $10\Omega$ resistor in the given circuit is $x$ volt.

The value of $x$ to the nearest integer is .

Q. A cell of internal resistance $r$ is connected to a load of resistance $R$. Energy is dissipated in the load but some thermal energy is also wasted in the cell. The efficiency of such an arrangement is found from the expression

$\frac{\text{Energy dissipated in the load}}{\text{Energy dissipated in the complete circuit}}$

Which of the following gives the efficiency in this case?

1. $\frac{r}{R}$
2. $\frac{R}{r}$
3. $\frac{r}{R+r}$
4. $\frac{R}{R+r}$

Q. Two electric bulbs $\text{A}$ and $\text{B}$ are rated $60\text{W}$ and $100\text{W}$ respectively. If they are connected in parallel to the same source, then
$($Assume bulb $\text{A}$ and $\text{B}$ have same voltage rating.)

1. Both the bulbs draw the same current.
2. Bulb $\text{A}$ draws more current than bulb $\text{B}$.
3. Bulb $\text{B}$ draws more current than bulb $\text{A}$.
4. Current drawn in the bulbs are in the ratio of their resistances.

Q. Two bulbs $40W$ and $60W$ and rated voltage $240V$ are connected in series across a potential difference of $420V$. Which bulb will work at above its rated voltage?

1. $40W$ bulb
2. Both will work
3. None of these
4. $60W$ bulb

Q. A $100\text{W}$ bulb designed to operate on $100\text{V}$ is to be connected across a $500\text{V}$ source. Find the resistance to be put in series, so that bulb consumes $100\text{W}$ only.

1. $500\Omega$
2. $100\Omega$
3. $400\Omega$
4. $200\Omega$

Q. A battery of internal resistance $4\Omega$ is connected to a network of resistances as shown in the figure. In order that the maximum power can be delivered to the network, the value of $R\left(\text{in}\Omega \right)$ should be-

1. $\frac{4}{9}$
2. $2$
3. $\frac{8}{3}$
4. $18$

Q. A wire when connected to 220V mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2$. Then $P_2:P_1$ is

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

Q. The wattage rating of a light bulb indicates the power dissipated by the bulb if it is connected across $110\text{V}$ DC potential difference. If a $50\text{W}$ and $100\text{W}$ bulb are connected in series to a $110\text{V}$ DC source, how much power will be dissipated in the $50\text{W}$ bulb?

1. $50\text{W}$
2. $100\text{W}$
3. $22\text{W}$
4. $11\text{W}$