Electrical Energy and Electrical Power

A potential $V_0$ is applied across a uniform wire of resistance $R.$ The power dissipation is $P_1.$ The wire is then cut into two equal halves and a potential of $V_0$ is applied across the length of each half. The total power dissipation across two wires is $P_2.$ The ratio of $P_2:P_1$ is $\sqrt{x}:1.$ The value of $x$ is _____.

Different combination of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is:

(A) 

(B) 

(C) 

(D) 

If a wire of resistance $R$ is connected across $V_0$, then power is $P_0$. The wire is cut into two equal parts and connected with $V_0$ individually, then sum of power dissipated is $P_1$, then $\frac{P_0}{P_1}$ is $\frac{1}{x}$. Find the value of $x.$

In the circuit given, consider $R_1=r$, $R_2=2r$ and power supply of voltage $V$.

Determine the power consumed by the circuit in each of the following instances:

i. when the switch is open

ii. when the switch is closed

iii. while the switch is closed, the resistor $R_2$ is heated so that its resistance is doubled.

An electric kettle has a power rating of $2000 \mathrm{W}$. It takes $90 \mathrm{seconds}$ to heat $500 \mathrm{g}$ water from $20 °\mathrm{C}$ to boiling. Use this information to calculate approximate value for the specific heat capacity of water.​

A metallic coil connected to a $220 \mathrm{V}$ supply, has a resistance of $110 \mathrm{\Omega }$ (while hot) How long will this coil take to heat $1 \mathrm{kg}$ of water from $20 °\mathrm{C}$ to $70 °\mathrm{C}$? Assume that whole of the heat produced by the coil is taken up by water. (Heat capacity of water= $4186 \mathrm{J}/\mathrm{kg} °\mathrm{C}$) 
 

Calculate the total power dissipated in the circuit.

In the circuit shown, a parallel combination of a coil of inductance $L$ and a resistance $R$ can be connected across a battery of electromotive force $\mathcal{E}$ and internal resistance $r$ through a switch. Find total heat dissipated in the resistance $R$ after the switch is closed.

In the given circuit when the switch is open, the ammeter $A$ reads $2.5 \mathrm{A}$, two of the four resistances dissipate $50 \mathrm{W}$ each and other two resistances dissipate $200 \mathrm{W}$ each. If the switch is closed and terminal voltage of the battery is so adjusted that the ammeter reading again becomes $2.5 \mathrm{A}$, find power dissipation in each of the resistances.

If voltage is applied between terminals $1$ and $2$ when terminals $3$ and $4$ are open, the power liberated is $P_1=40 \mathrm{W}$ and when terminals $3$ and $4$ are connected, the power liberated is $P_2=80 \mathrm{W}$. If the same source is connected to the terminals $3$ and $4$, the power liberated in the circuit when terminals $1$ and $2$ are open is $P_3=20 \mathrm{W}$. Determine the power $P_4$ consumed in the circuit when the terminals $1$ and $2$ are connected and the same voltage is applied between the terminals $3$ and $4$.

For what value of $\epsilon$ power across $4\mathrm{\Omega }$ will be $100 \mathrm{W}$?

In two - seemingly alike - electric kettles the heating wire is bent into the shape of a regular hexagon. In one of the kettles the heating element was connected as shown in figure a), whilst in the other the heating element was connected as shown in figure b). The ratio of time taken in case a) to case b) is

An electrical bulb rated $220 \mathrm{V},100 \mathrm{W}$, is connected in series with another bulb rated $220 \mathrm{V}$, $60 \mathrm{W}$. If the voltage across combination is $220 \mathrm{V}$, the power consumed by the $100 \mathrm{W}$ bulb will be about _____ $\mathrm{W}$.

Given below are two statements :
Statement I : A uniform wire of resistance $80 \mathrm{\Omega }$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5 \mathrm{\Omega }$.

Statement II : Two resistance $2R$ and $3R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3R$ and $2R$ will be in the ratio $3:2$.

In the light of the above statements, choose the most appropriate answer from the options given below

A direct current of $4 \mathrm{A}$ and an alternating current of peak value $4 \mathrm{A}$ flow through resistance of $3 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

The charge flowing through a resistor $R=2 \mathrm{\Omega }$ varies with time as $q=3-4t^2$. The heat produced in $2$ second is about (where $q$ is in $C$ and $t$ is in $S$)

A $220 \mathrm{V},50 \mathrm{Hz}$ AC source is connected to a $25 \mathrm{V},5 \mathrm{W}$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be

A resistor develops $300 \mathrm{J}$ of thermal energy in $15 \mathrm{s}$, when a current of $2 \mathrm{A}$ is passed through it. If the current increases to $3 \mathrm{A}$, the energy developed in $10 \mathrm{s}$ is _____ $\mathrm{J}$.

A bulb of $100 \mathrm{W}$ rating is connected with $220 \mathrm{V}$ supply. The resistance of bulb is

The emf of a car battery is $12 \mathrm{V}$. If internal resistance of battery is $0.4 \mathrm{\Omega }$, then maximum power drawn from battery is _____ $\mathrm{W}$.