Question Video: Finding the Resistance of a Resistor Connected in Series | Nagwa Question Video: Finding the Resistance of a Resistor Connected in Series | Nagwa

Question Video: Finding the Resistance of a Resistor Connected in Series Physics • Third Year of Secondary School

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 2𝑅, and the third resistor has a resistance of 3𝑅. The cell provides a potential difference of 24 V. The current through the circuit is 0.1 A. What is the value of 𝑅?

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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.

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