Video Transcript
The resistor in the circuit shown
is powered by two batteries connected in parallel. One battery has a terminal voltage
of 2.5 volts. What must be the terminal voltage
of the other battery for the potential drop across the resistor to be
determinable?
To answer this question, we will
use Kirchhoff’s second law. Recall that Kirchhoff’s second law
states that the sum of the potential differences across each component in a loop in
a circuit is equal to zero. Consider the loop that we’ve
highlighted in the part of the circuit containing the batteries in parallel. By applying Kirchhoff’s second law
to this loop, we find that 2.5 volts minus the unknown voltage 𝑉 of the battery on
the lower branch must equal zero.
We can solve this equation for the
unknown voltage by adding 𝑉 to both sides. We then have that 2.5 volts is
equal to the unknown voltage 𝑉. That is, the terminal voltage of
the battery on the lower branch is equal to 2.5 volts. This makes sense because in order
to obey Kirchhoff’s second law, batteries in parallel need to have identical
terminal voltage. Thus, because one of the batteries
in parallel has a terminal voltage of 2.5 volts, we know that the terminal voltage
of the other battery must also be 2.5 volts.