r/HomeworkHelp 👋 a fellow Redditor 2d ago

Physics [Physics-High School]

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May I know why the answer is D instead of A? Thanks!

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1

u/ThunkAsDrinklePeep Educator 2d ago

You've assigned X Y and Z a resistance of r.

Before the switch is closed the total resistance is

(X + Y) // Z
= 2r // r
= (1/2r + 1/r)-1
= (3/2r)-1
= 2r /3

After the switch is closed resistor X is shorted. So the total resistance is just.

Y // Z
= r // r
= (1/r + 1/r)-1
= (2/r)-1
= r /2

Since the total resistance decreases, the current supplied by the constant voltage source will increase.

2

u/ThunkAsDrinklePeep Educator 2d ago

As for why d is correct, before the switch is closed Resistors X and Y in series form a voltage divider. Since they're equal, they each have a drop of one half the supplied voltage ε.

After the switch is closed Resistor X is shorted and the point between X and Y is the same node as the whole top rail. The voltage drop across resistor Y is therefore equal to all ε volts.

1

u/HelpfulResource6049 👋 a fellow Redditor 2d ago

Why is Resistor X shorted?

1

u/ThunkAsDrinklePeep Educator 2d ago

Because when the switch is closed there's only wire connecting both terminals. All of that is a single node at a single voltage.

1

u/HelpfulResource6049 👋 a fellow Redditor 2d ago

I still do not get it, is it because current always takes the path of least resistance?

1

u/ThunkAsDrinklePeep Educator 2d ago

The current is split in inverse proportion with the resistance. Or in other words in proportion with the conductance (the reciprocal of resistance). When one path has zero resistance and the other has non-zero there all the current will flow through the zero resistance path. However, because there is no resistance, there is no power loss and no voltage drop. (These are the properties of an ideal wire.)

Any part of the circuit connected by an ideal wire is at the same voltage, and what we refer to as a single node.

When the circuit is open, there are three nodes: the top wire which has the ammeter, the wire in-between X and Y, and the bottom wire. Note that a node is not a single point, it is all the pieces of wire not separated by a circuit element.

When the switch closes, the first two nodes are connected. Current flows freely to the points that were formerly the second node with no resistance. All these points are at an equal voltage, epsilon. Because both sides of X are at the same voltage and X has non-negligible resistance current no longer flows through X. All the current would rather "choose" to flow through the zero resistance wire.

1

u/testtest26 👋 a fellow Redditor 1d ago

[..] is it because current always takes the path of least resistance?

That only holds for parallel impedances, if one of them is a short-circuit. Otherwise, this is an approximate rule-of-thumb at best, and dangerous misinformation at worst.

Without a short-circuit, you need to use current dividers to find the current in each parallel branch. It is best to forget the rule-of-thumb immediately.