Question

When both the current and voltage in a circuit are doubled, what happens to resistance and power?

Answer 1

Hint: To solve this type of problem first we have to write the respective relation. Write the relation between voltage, current and resistance to see the change in the resistance due to increase in voltage and current. Then write the relation between the voltage, current and power to see the change in the resistance due to increase in voltage and current.

Complete step by step answer:
Let us assume a current flows through a circuit be $I$ and the voltage of the circuit be $V$.
Now from ohm’s law we can say resistance is the ratio of current flow to voltage across it.
Mathematically,
$R = \dfrac{V}{I} \ldots \ldots \left( 1 \right)$
Now as per the given problem both current and voltage in the circuit are doubled or we can say increase by two times.
Hence the new voltage and current will be,
$V' = 2V$
$I' = 2I$
Where,
$V'\,\,and\,\,I'$ are the changed voltage and current respectively.
Now the new resistance be,
$R' = \dfrac{{V'}}{{I'}}$
Now putting the respective values we will get,
$R' = \dfrac{{2V}}{{2I}}$
On cancelling common term and using equation $\left( 1 \right)$ we will get,
$R' = R$
Now for the power it is represented as the product of voltage and current.
Mathematically,
$P = VI \ldots \ldots \left( 2 \right)$
Now as per the given problem both current and voltage in the circuit are doubled or we can say increase by two times.
Hence the new voltage and current will be,
$V' = 2V$
$I' = 2I$
Where,
$V'\,\,and\,\,I'$ are the changed voltage and current respectively.
Now the new power be,
$P' = V'I'$
Now putting the respective values we will get,
$P' = 2V \times 2I$
On cancelling common term and using equation $\left( 2 \right)$ we will get,
$P' = 4P$
Hence we can conclude that when both the current and voltage in a circuit are doubled the resistance of the circuit will remain the same, but the power of the circuit becomes four times.

Note: Remember that resistance measures the opposition to current flow in an electric circuit and it is measured in ohm which is symbolized by the Greek symbol $\Omega $. An electric power is the rate per unit time at which an electric energy is transferred by an electric circuit which is measured in Watt and symbolized by $W$.