Video Transcript
The circuit diagram represents a
galvanometer combined with a shunt resistor. The emf of the cell connected to
the galvanometer and the shunt is 3.0 volts. The diagram does not represent a
circuit in which the galvanometer and shunt function correctly as an ammeter. What is the difference between the
potential difference across the shunt and the potential difference across the
galvanometer?
So, in this question we’re
comparing potential differences across two components that are connected in
parallel: a galvanometer and a shunt resistor. We can label the potential
difference across the galvanometer 𝑉 𝐺 and the potential difference across the
shunt resistor 𝑉 𝑆.
Now, the question tells us that the
emf of the circuit’s cell is 3.0 volts. However, we don’t know the
resistance of the shunt resistor or the resistance of the galvanometer, nor do we
know anything about the current in the circuit. Actually, though, we don’t need to
know those values, or any other numerical values, to solve this question. All we need to do is recall the
fact that parallel branches in a circuit have the same potential difference across
them. Because of this, we know that 𝑉 𝐺
must be equal to 𝑉 𝑆.
Now, the question is asking us to
find the difference between the potential difference across the shunt resistor and
the potential difference across the galvanometer. Since we know that these quantities
are equal, then there must be no difference between them. We can show this algebraically by
subtracting 𝑉 𝑆 from both sides of this equation, which gives us 𝑉 𝐺 minus 𝑉 𝑆
equals zero. In other words, the difference
between 𝑉 𝐺 and 𝑉 𝑆 is zero.
Now, since we measure potential
differences in volts, then our final answer for the difference between the potential
difference across the galvanometer and the potential difference across the shunt
resistor is zero volts.
