Question

A resistor dissipates 0.5 W when a potential difference of 4.0 V is applied. When the potential difference is changed such that the power dissipated increases to 2.0W, what is the current, in A, through the resistor at the new potential difference?

Answer 1

I = 0.25 A

Step-by-step explanation:

Resistors

The resistors are the circuit elements that oppose the flow of the current. The more resistance an element has, the less current is allowed to go through it. For a resistor of resistance R to which a voltage V is applied, the equation for the current is given by the Ohm's law:

`\displaystyle I=(V)/(R)`

The power dissipated by a resistor R is given by the Joule's law

`P=I^2R`

Replacing the first equation into the second, we have

`\displaystyle P=(V^2)/(R)`

The question refers to a resistor that dissipates P=0.5 W when 4 Volts are applied to it, thus we can compute R solving the above equation for R

`\displaystyle R=(V^2)/(P)=(4^2)/(0.5)=32\Omega`

If the voltage is changed such that the new power dissipated by the resistor is 2 W, we can compute the new current, solving the equation of Joule's law for I

`\displaystyle I=\sqrt{(P)/(R)}=\sqrt{(2)/(32)}=0.25\ A`