How to find the heat energy produced in a resistor?

[ellieee]

Homework Statement

nil

Relevant Equations

I=Q/t

i found current to be 2/5 A. then 2/5A multipled by 6s = 2.4C. and since one joule per coulomb is equal to the unit of p.d, i get 2.4J. I don't get 4.8J(supposed answer)

 

[Steve4Physics]

... then 2/5A multipled by 6s = 2.4C. and since one joule per coulomb is equal to the unit of p.d, i get 2.4J

The last step is where you went wrong.

Having 2 volts means that 2 joules of energy are transferred per coulomb.
Does that help?

A better way to do these sorts of problems is using simple formulae. The key formula relating energy transferred (E, in joules) when charge (Q in coulombs) flows through a potential difference (V in volts) is:

E = QV (worth learning)

Other handy formulae are V = IR and Q = It.

Another approach is to find the power (using an appropriate formula). Then, using the time, you can find the energy easily. But I don’t know which method you are expected to use.

 

[Chestermiller]

Another way of approaching this is that the rate of heating is $\frac{V^2}{R}$.

 

[berkeman]

Another way of approaching this is that the rate of heating is $\frac{V^2}{R}$.

Agreed. I prefer to do problems the simplest way if possible, and not do extra calculations. Since we are given the Voltage and Resistance, that gives us the power directly as you say. Then just multiply by the time of 6 seconds to get the energy.

$$P = \frac{V^2}{R} = \frac{2^2}{5} = \frac{4}{5} [Watts]$$
$$Heat Energy = Power * Time = \frac{4}{5} [Watts] * 6 [seconds] = 4.8 [Joules]$$