You can use the rule already: in a series circuit, the component voltages add up to the source voltage. But why do they add up, rather than anything else?
Earlier in this course you saw that energy is conserved, with heat and light counted in: the full energy ledger always balances. That balance is about to explain the rule.
6 V means the battery gives each coulomb of charge 6 J of energy.
Follow one coulomb around one complete trip.
Passing through the resistor, the coulomb transfers 4 J. The resistor warms up.
Passing through the bulb, the coulomb transfers its remaining 2 J. The bulb gives out light and heat.
4 J + 2 J = 6 J: the coulomb transfers exactly the energy the battery gave it.
Energy is conserved, so this ledger balances on every trip: the energy gained from the source equals the total energy transferred in the components.
A 12 V source drives two bulbs in series, and the bulb voltages add to 12 V. Why must they add up like this?
Now turn the ledger into voltages. The energy gained per coulomb is the source voltage: 6 V. The energy transferred per coulomb in each component is that component's voltage: 4 V across the resistor, 2 V across the bulb.
So 4 V + 2 V = 6 V. The voltage shares add up to the source voltage.
Noor says that by the time a coulomb returns to the battery, it has transferred all the energy the battery gave it. Is Noor correct?
A 9 V battery drives a motor and a buzzer in series. Each coulomb transfers 5 J in the motor and 4 J in the buzzer. Show that the coulomb's energy ledger balances.
Write down the energy gained:
9 V means 9 J gained per coulomb from the battery
Write down the energy transferred:
5 J in the motor, 4 J in the buzzer
Add the transfers:
5 + 4 = 9
Each coulomb transfers 9 J in total, exactly the 9 J it gained. The ledger balances.
A source gives each coulomb 7.5 J. The loop holds two components, and the first transfers 4.5 J per coulomb. How many joules does the second transfer per coulomb?
A 24 V supply drives three resistors in series, and their voltages add to 24 V. Which statement explains why?
Which conservation law explains why the component voltages in a series circuit add up to the source voltage?
A 10 V source drives two components in series. Component X transfers 6 J to each passing coulomb. How much energy does each coulomb transfer in component Y?