### Video Transcript

The potential difference across a resistor in a circuit is 10 volts. If 150 coulombs of charge passes through the resistor, how much energy is dissipated to the environment by the resistor?

Okay, so we’ve got a circuit containing a resistor, and we’re told that the potential difference across that resistor is 10 volts. Let’s label this potential difference as 𝑉. We’ll label the charge that passes through the resistor as 𝑄. And we’re told that this is equal to 150 coulombs.

The question is asking us to work out how much energy the resistor dissipates to the environment. We can recall that there’s a formula which links the electrical energy dissipated by a component, the charge that passes through that component, and the potential difference across the component. Specifically, the electrical energy 𝐸 is equal to the amount of charge 𝑄 multiplied by the potential difference 𝑉 across which the charge moves.

We know the values of the charge 𝑄 and the potential difference 𝑉, so we can go ahead and substitute them into this equation to calculate the electrical energy 𝐸. When we do this, we find that 𝐸 is equal to 150 coulombs, that’s our value for 𝑄, multiplied by 10 volts, our value for 𝑉.

Now we just need to evaluate this expression for the energy 𝐸. When we have a charge in units of coulombs and a potential difference in units of volts, this will give us an energy in units of joules. Evaluating the expression, we find that this energy has a value of 1500 joules. So our answer to the question is that the amount of energy dissipated to the environment by the resistor is 1500 joules.