Electrical working in series circuits

How to find the power dissipated in circuits with only series connections

In episode 01 you saw how to find the current in this loop (with only series connections like this, there is only one value for the current), using the relationship I = VR and then the potential differences across the lamps, using the constraining relationships V₁ = R₁ × I and V₂ = R₂ × I.

Now you need only add to this analysis to find out the power dissipated in each lamp. This value is the power in the electrical working pathway, calculated by P = I × V.

But, and it can be a big but, you need to take great care to use the correct values of V and I. Careful and explicit labelling will help you and those you teach to keep a clear head.

We emphasise again that V, I and R, without modifiers, are best reserved for entire circuits.

Keeping the calculations in order

You have to repeat a sum with variations two or three times, depending on how much you remember about the conservation of energy:

For the top lamp, P₁ = I × V₁.

For the bottom lamp, P₁ = I × V₁.

For the cell, P = I × V.

Now start with E = E₁ + E₂, which is just the conservation of energy, and remember that the energy shifted in any one second is just the power.

You'll get P = P₁ + P₂, and you could use this relationship in place of one of the three multiplications.

You might like to review the process by completing the model provided in the support sheet (see below).