Video Transcript
A galvanometer and a shunt resistor
are connected in parallel to form an ammeter. The resistance of the shunt is 𝑅
𝑆 and the resistance of the galvanometer is 𝑅 𝐺. The current in the shunt is 𝐼 𝑆
and the current in the galvanometer is 𝐼 𝐺. Which of the following correctly
relates these values? (A) 𝑅 𝑆 over 𝑅 𝐺 equals 𝐼 𝐺
over 𝐼 𝑆. (B) 𝑅 𝑆 over 𝑅 𝐺 equals 𝐼 𝑆
over 𝐼 𝐺.
To help us think about this
question, let’s consider the form of an ammeter. When electric charge flows through
an ammeter, it passes through two parallel branches, one with a galvanometer and
another with a shunt resistor. If we want to relate the individual
values of the resistance and current at the resistor and galvanometer to each other,
we’ll have to recall Ohm’s law. Let’s choose a form that relates
everything to potential difference 𝑉.
Ohm’s law can be written as 𝑉
equals 𝐼𝑅, where 𝑉 is the potential difference, 𝐼 is the current, and 𝑅 is the
resistance. If we specifically use Ohm’s law
across the shunt resistor, we find that 𝑉 𝑆 equals 𝐼 𝑆 𝑅 𝑆. Similarly, using Ohm’s law across
the galvanometer, we get 𝑉 𝐺 equals 𝐼 𝐺 𝑅 𝐺.
Now, looking back at our diagram,
let’s recall that parallel branches in circuits will have the same potential
difference across each branch. This means that when we connect a
shunt resistor in parallel with the galvanometer, the potential difference across
the shunt resistor will be equal to the potential difference across the
galvanometer. This means that 𝑉 𝑆 equals 𝑉
𝐺.
We can now substitute these
specific potential differences with their relations to current and resistance. And we find that 𝐼 𝑆 𝑅 𝑆 equals
𝐼 𝐺 𝑅 𝐺. From here, dividing both sides by
𝑅 𝐺, we get 𝐼 𝑆 𝑅 𝑆 divided by 𝑅 𝐺 equals 𝐼 𝐺. And then dividing both sides by 𝐼
𝑆, we get 𝑅 𝑆 divided by 𝑅 𝐺 equals 𝐼 𝐺 divided by 𝐼 𝑆.
So now we have an equation that
relates the resistances of the shunt and galvanometer with their currents. And we can see that this answer
corresponds with option (A). Therefore, option (A) is the
correct answer that relates these values together.
