Question

Find the new power dissipated in the resistor if the resistance of $12\Omega $ is connected to the battery and current is doubled. The current in the resistor is $0.2A$.
A) $0.48W$
B) $0.96W$
C) $1.92W$
D) $4.8W$

Answer 1

-Hint:- As given that, current is doubled so, $I' = 2I$
Now, we have to calculate the new power using the expression –
$P = VI$
(where, $V$ is the voltage and $I$ is the new current in the resistor)

Complete Step by Step Solution: -
Let the current in the resistor be $I$ and the new current after doubling be $I'$
Therefore, as mentioned in question that the current is now doubled so, we can get the new current in the resistor by –
$I' = 2I$
According to the question, it is given that
$I = 0.2A$
$
  \therefore I' = 2 \times 0.2 \\
  I' = 0.4A \\
 $
To calculate the power, we have to use the expression –
$P = VI' \dots (1)$
But, we don’t have the value of voltage $V$ so, we have found the expression of power which uses the value of resistance as it is given in question and value of current.
From equation $(1)$
$P = VI'$
We know that, by ohm’s law
$V = I'R \cdots (2)$
where, $R$ is the resistance in the circuit
Substituting the value of $V$ from equation $(2)$ in equation $(1)$
Therefore, in equation $(1)$, we get
$P = {(I')^2}R \cdots (3)$
Putting the values of current and resistance in equation $(3)$, we get
$
  P = {(0.4)^2} \times 12 \\
  P = 0.16 \times 12 \\
 $
By further calculations, we get
$P = 1.92Watt$

Therefore, the correct answer for this question is option (C).

Note:- Ohm’s law is the relationship between current, resistor and potential difference. Ohm’s law states that potential difference across the ends of conductor is directly proportional to the current of the conductor. Mathematically, it can be represented as –
$
  V ∝ I \\
  V = IR \\
 $
Ohm’s law does not work for those electrical components that have the flow of electricity in one direction only.