Resistors in parallel and series

[ehabmozart]

Homework Statement

If an ohmmeter is connected between points and in each of the circuits shown in the figure . For the circuit a) what will it read? For the circuit b) what will it read?

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Homework Equations

Series and Parallel rules

The Attempt at a Solution

I need help just in part b. Now, when we combine the 30 and 45 resistors, the solution manual combines them in parallel and the equivillant is drawn on the bottom line. My question is WHERE DID THE WIRE IN THE MIDDLE GO? Did it miraculously dissapear?... I need tips in knowing how to determine parallel in series.. ? Thanks for any help

 

[Doc Al]

What middle wire? Unless the wires (and the connections) are labeled, we'll have a difficult time discussing them.

In any case, if you can pick two points and redraw the wires such that the 30 and 45 resistors are in parallel between them (and you can), then you are justified in replacing them with the equivalent.

 

[ehabmozart]

What middle wire? Unless the wires (and the connections) are labeled, we'll have a difficult time discussing them.

In any case, if you can pick two points and redraw the wires such that the 30 and 45 resistors are in parallel between them (and you can), then you are justified in replacing them with the equivalent.

I mean here the wire at which the 30 ohm resistor is placed. When drawn equivilantly with the 45 ohm resistor, they put them on the very bottom line and take off the wire which the 30 ohm resistor was originally placed at!

 

[Doc Al]

I mean here the wire at which the 30 ohm resistor is placed. When drawn equivilantly with the 45 ohm resistor, they put them on the very bottom line and take off the wire which the 30 ohm resistor was originally placed at!

Still not clear where the problem is.

In your diagram, look at the rectangle that contains the two resistors. Label the corners a, b, c, d, starting with the upper left and going clockwise. Would you not agree that a,b, and c are essentially the same point? And thus between that point and point d, the two resistors are in parallel.

 

[Nickie]

I would like to clarify that resistors in parallel and series refer to the arrangement of resistors in an electrical circuit. In series, the resistors are connected end-to-end, while in parallel, they are connected side by side. The rules for calculating the equivalent resistance in series and parallel are based on Ohm's law and Kirchhoff's laws.

In the given circuits, the ohmmeter is connected between points A and B. In circuit a), the resistors are connected in series, so the ohmmeter will read the sum of the resistances (10Ω + 20Ω = 30Ω). In circuit b), the resistors are connected in parallel, so the equivalent resistance is calculated using the formula 1/Req = 1/R1 + 1/R2. Therefore, the ohmmeter will read a value less than 30Ω, as the resistors are effectively working together to reduce the overall resistance.

As for the question about the wire in the middle, it does not disappear. In circuit b), the resistors are connected in parallel, which means they have a common connection point at the bottom. The wire in the middle is simply a representation of this common connection point. You can think of it as a "junction" where the current splits into two paths and then comes back together at the other end.

To determine whether resistors are connected in series or parallel, you can follow these steps:
1. Trace the path of the current from one end of the circuit to the other.
2. If the current passes through each resistor one after the other, they are connected in series.
3. If the current splits into multiple paths and then comes back together, the resistors are connected in parallel.

I hope this helps in understanding resistors in parallel and series.