Question

When a potential difference of \[20V\] is connected across an unknown resistor, it dissipates\[10W\] of power. If a current of \[5A\] is passed through the same resistor. The power dissipated will be

Answer 1

Hint: In order to solve this question, we are going to first calculate the value of the unknown resistance by using the relation between power dissipated and voltage. After that using the value of the resistor, the power dissipated for the given current is calculated by using the formula for it.

Formula used:
The formula for the power dissipated is given as
\[P = \dfrac{{{V^2}}}{R}\]
Where, \[R\]is the resistance of the unknown resistor, and \[V\]is the voltage.
The power dissipated for the current\[I\]is given as
\[P = {I^2}R\]


Complete step-by-step solution:
It is given in this question that the potential difference across the unknown resistance is equal to
\[V = 20V\]
Also, it is given that the power dissipated is given as
\[P = 10W\]
We know that the formula for the power dissipated is given as
\[P = \dfrac{{{V^2}}}{R}\]
Where, \[R\]is the resistance of the unknown resistor
Putting the values of voltage and power in the above equation,
\[10 = \dfrac{{{{\left( {20} \right)}^2}}}{R}\]
Solving this to get the value of the resistance
\[R = \dfrac{{{{\left( {20} \right)}^2}}}{{10}} = \dfrac{{400}}{{10}} = 40\]
We need to find the power dissipated when the current is equal to
\[I = 5A\]
And the resistance is found as \[R = 40\Omega \]
Thus, the power is calculated as
\[P = {I^2}R\]
Putting the values, we get
\[P = {\left( 5 \right)^2} \times 40 = 25 \times 40 = 1000W\]
Thus, the power dissipated will be equal to \[1000W\]and the unknown resistance is of the value\[40\Omega \]

Note: It is important to note that the value of the unknown resistor remains the same even when the current or the voltage is changed. This fact has been used by taking the two different formulas for the power related to the voltage and the current to find the power for the current given in the question.