Video Transcript
The circuit shown in the diagram
consists of three resistors connected in series with a cell. The first resistor has a resistance
of 𝑅, the second resistor has a resistance of two 𝑅, and the third resistor has a
resistance of three 𝑅. The cell provides a potential
difference of 24 volts. The current through the circuit is
0.1 amps. What is the value of 𝑅?
When components are connected in
series, their resistances can be treated as if they were a single component with an
equivalent resistance. So the three resistors can be
replaced with a single resistor with a resistance 𝑅 sub total as seen in this
diagram. Now, we can recall that the total
resistance of components connected in series is given by the following equation,
where 𝑅 one is the resistance of the first component, 𝑅 two is the resistance of
the second component, and so on. This series circuit contains three
resistors. So the total resistance in this
case is given by 𝑅 plus two 𝑅 plus three 𝑅. This is equal to six 𝑅. So the total resistance of the
three resistors connected in series is equivalent to a single resistor of resistance
six 𝑅.
We can now calculate the value of
𝑅 using Ohm’s law. Recall that Ohm’s law is given by
𝑉 equals 𝐼 times 𝑅 sub total, where 𝑉 is the total potential difference, 𝐼 is
the total current, and 𝑅 sub total is the total resistance. We can substitute in the value of
the total resistance into this equation and we get 𝑉 equals 𝐼 times six 𝑅. If we now divide both sides by six
𝐼, this cancels out on the right-hand side. And we find that 𝑅 is given by 𝑉
divided by six 𝐼. 𝑉 is equal to the potential
difference of the cell, which is given as 24 volts. 𝐼 is equal to the current through
the circuit, which is given as 0.1 amps. Therefore, 𝑅 is equal to 24 volts
divided by six times 0.1 amps. This is equal to 40 ohms.
So, the value of 𝑅 is 40 ohms.
