WEBVTT
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The diagram shows a circuit consisting of a cell and two resistors connected in series.
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If the total resistance of the circuit is 20 ohms, what is the value of π
?
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So this question shows us a circuit diagram in which we have two resistors connected in series.
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This means that theyβre connected one after the other along the same loop.
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The right-hand resistor has a resistance of seven ohms.
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Meanwhile, the left-hand resistor is labeled with a resistance of π
.
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We are asked to work out the value of π
given that the total resistance of the circuit is 20 ohms.
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This total resistance of the circuit is equal to the resistance of both of these two resistors together.
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So letβs recall what happens when we have two resistors connected in series.
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To do this, weβll consider two general resistors, one with a resistance of π
one, the other, a resistance of π
two.
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When the two resistors π
one and π
two are connected in series, the total resistance of both of them together, which weβve labeled as π
subscript π, is equal to π
one plus π
two.
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In other words, whenever we have two resistors connected in series, their total resistance is equal to the sum of the individual resistances.
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So letβs apply this knowledge to the circuit from the question.
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Weβre told that the total resistance is 20 ohms.
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And because this value is the resistance of these two resistors connected in series, then we know that this 20 ohms must be equal to the resistance π
plus the resistance of seven ohms.
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This leads us to this equation here, which we can use to find the value of π
.
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We want to make π
the subject of the equation.
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So letβs subtract seven ohms from each side.
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On the left-hand side, we have 20 ohms minus seven ohms, which gives us 13 ohms.
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On the right-hand side, we have π
plus seven ohms minus seven ohms, which is simply equal to π
.
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And so we have found our answer to the question that the value of π
is equal to 13 ohms.