Question

The value power $P_1$ is

A. 1000W
B. 975W
C. 25W
D. 200W

Answer 1

The equation of power is useful here .we can use different equations of power to find it. Here, the circuit is in series connection. So the total power will be the sum of two individual powers. Power is the work done in unit time. That means how much energy has been used within a short span of time.

Complete answer:
First of all we have to understand the equations of power.
$\begin{aligned} & P=EI \\\ & P={{I}^{2}}R \\\ \end{aligned}$
Where, E is the voltage supplied to the circuit.
I is the current flowing through the circuit.
R is the Resistance.
Now, let us find the current flowing through the circuit. Current is given by the ohms law as,
$I=\dfrac{V}{R}$
Here, the resistance is in series connection. So,
$R={{R}_{1}}+{{R}_{2}}=1+39=40\Omega$
Now, current will be given as,
$I=\dfrac{V}{R}=\dfrac{E}{R}=\dfrac{200}{40}=5A$
We know that total power of the combination will be,
$\begin{aligned} & P={{I}^{2}}R \\\ & \Rightarrow P={{\left( 5 \right)}^{2}}\times 40=1000W \\\ \end{aligned}$
Therefore total power = 1000W
Now let’s find power dissipated at the first bulb. The resistance of the first bulb is 1 ohm. So,
$\begin{aligned} & {{P}_{1}}={{I}^{2}}R \\\ & \Rightarrow {{P}_{1}}={{\left( 5 \right)}^{2}}\times 1=25W \\\ \end{aligned}$
Therefore the power dissipated at the first bulb is ${{P}_{1}}=25W$.

So, the correct answer is “Option C”.

Additional Information:
power is the force acting per unit time period. Power is the amount of force applied in a short period of time. The S.I unit of power is watt. The concept of power is having a great role in our daily life. Electric power is measured in kilowatt hour.
Power can be represented by so many equations like,
$\begin{aligned} & P=F\times \upsilon \\\ & P=\dfrac{E}{t} \\\ & P=V\times I \\\ & P={{I}^{2}}\times R \\\ & P=\dfrac{{{V}^{2}}}{R} \\\ \end{aligned}$
Power can be found out by multiplying force and velocity. Power is the energy per unit time. So by that way also we can find the value of power. Another way to find power is the product of the square of current and resistance of the material used. Current term can be replaced by voltage by the usage of ohm’s law.
So basically power is energy involved per time period. In physics more power means more energy can be used up in a very short span of time. Value of power decreases as the time span increases.

Note:
The power can be found out easily, Even though the unit of the current, voltage and resistance should be noted well. Faults in their units may lead to wrong answers.