Video: Physics Past Exam • 2017/2018 • Pack 1 • Question 21B

Physics Past Exam • 2017/2018 • Pack 1 • Question 21B

02:32

Video Transcript

The figure shows a branching point in an electric circuit. Find the current in branch 𝑥 and the direction of the current in branch 𝑦.

Looking at our figure, we see branches 𝑥 and 𝑦. Branch 𝑦 has a current of 10 amps running through it. But we’re not sure whether that current approaches or moves away from the node. And branch 𝑥 has a current we know moves towards the branching point. But we don’t know the magnitude of that current 𝐼. We want to solve for both 𝐼 as well as the direction of the current in branch 𝑦.

To do all this, we’ll use a principle of closed circuits sometimes called Kirchhoff’s node rule. What this node rule tells us is that the sum of all current entering and leaving a branching point is zero. That means if we add up all the current going into this branching point, that’s equal to all the current going out of that point. Notice that this rule is essentially a statement of the conservation of charge, that we can’t have charge building up at any one point in the circuit.

Let’s apply this rule to our particular branching point to solve for the magnitude of 𝐼 as well as the direction of the current in branch 𝑦. As we do, we’ll adopt the convention that current that’s leaving the branching point will have a negative value to it and current that’s going into the branching point will have a positive value to it. Here then is the equation we can write when we consider all these currents going into and out of the branching point.

We can say that negative eight amps plus two amps plus four amps plus nine amps plus or minus 10 amps, because we’re not yet sure of the direction of the current in branch 𝑦, plus 𝐼 is all equal to zero. If we combine together the four current whose sign and magnitude we know, they all reduce down to seven amperes. So now, our equation reads: seven amps plus or minus 10 amps plus 𝐼 is equal to zero.

Here is what we have then. We have two positive values, seven amps and 𝐼, added together to a third value to give zero. That tells us that this third value must be less than zero in order for the sum to be zero. So the 10-amp current is moving in the negative direction, that is away from our branching point.

Now that we know the direction of the current in branch 𝑦, we can solve for the magnitude 𝐼 by subtracting seven amps from 10 amps. We find that the current 𝐼 is equal to three amps. Here then is what we can say in answer to our question. We can say that the current in branch 𝑥 is three amps and the current in branch 𝑦 is away from the node. That’s how the current in the 𝑥 and 𝑦 branches behaves.

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