Power Delivered and Heat Dissipated in a Circuit

Q. A battery of emf E and internal resistance r is connected to a resistor of resistance $r_1$ and Q joules of heat is produced in a certain time t. When the same battery is connected to another resistor of resistance $r_2$ the same quantity of heat is produced in the same time t the value of r is

1. $\frac{r_1^2}{r_2}$
2. $\frac{r_2^2}{r_1}$
3. $\frac{1}{2}(r_1+r_2)$
4. $\sqrt{r_1{r}_2}$

Q.

In an ac circuit with voltage $V$ and current $I$, the power dissipated is.

1. $VI$

2. $\frac{VI}{2}$

3. $\frac{VI}{\sqrt{2}}$

4. Depends on the phase between $V$ and $I$

Q. A resistor develops 1600 J of thermal energy in 50 s when a current of 2 A flows through it. If the current is increased to 10 A, what will be the thermal energy developed in the same amount of time?

1. 40 KJ
2. 16 KJ
3. 80 KJ
4. 64 KJ

Q. A cell of emf $1.5V$ having a finite internal resistance is connected to a load resistance of $2\Omega$. For maximum power transfer, the internal resistance of the cell should be

1. $4\Omega$
2. $0.5\Omega$
3. $2\Omega$
4. None of these

Q. What is the power in the given circuit?

1. 3.6 W
2. 35 W
3. 175W
4. 245W

Q. In the meter bridge experiment shown in figure, the balance length AC corresponding to null deflection of the galvanometer is x. What would be the balance length if the radius of the wire AB is doubled?

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

Q. A cell of emf $1.5V$ having a finite internal resistance is connected to a load resistance of $2\Omega$. For maximum power transfer, the internal resistance of the cell should be

1. $4\Omega$
2. $0.5\Omega$
3. $2\Omega$
4. None of these

Q. A current i = 2 + 3$\sin \left(2\pi {10}^{3}t\right)$ is flowing through a resistance of value $4\Omega$. Heat generated in kilo joules in 3 minutes across the resistance is (Write up to two digits after the decimal point)

Q. A resistor of resistance R is connected to an ideal battery (battery with zero internal resistance). If the value of R is increased, the power dissipated in the resistor will___?

1. increase
2. decrease
3. remains unchanged
4. Data insufficient

Q. A constant voltage is applied between the two ends of a metallic wire. Some heat is developed in it. The heat developed is doubled if

1. both the length and the radius of the wire are halved
2. both the length and the radius of the wire are doubled
3. the radius of the wire is halved
4. the length of the wire is doubled

Q. Six similar bulbs are connected as shown in the figure with a DC source of emf $E$ and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) when two from section 'A' and one from section 'B' are glowing, will be

1. 4 : 9
2. 9 : 4
3. 1 : 2
4. 2 : 1

Q. If the length of the filament of a heater is cut by $10\%$ and removed, the power of the heater will

1. Increase by about $9\%$
2. Increase by about $11\%$
3. Increase by about $9\%$
4. Decrease by about $10\%$

Q. Power dissipated in a resistor is to resistance when current through it is constant, and to resistance when voltage across it is constant.

1. proportional
2. inversely proportional
3. equal
4. unsusceptible

Q. Power dissipated in a resistor is to resistance when current through it is constant, and to resistance when voltage across it is constant.

1. proportional
2. inversely proportional
3. equal
4. unsusceptible

Q. An electric bell has a rating of 500 W 100 V. It is used in a circuit having a 200 V supply. What resistance must be connected in series with the bulb so that it delivers 500 W?

1. 10 ohm
2. 20 ohm
3. 30 ohm
4. 40 ohm

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. $I-Q,II\to T,III\to U,IV\to R$