# problem whith circuit

#### Jeff18

I need help to solve this problem. Can anyone help me to solve this exercise? I can not really solve it. The source is Halliday.

Prove that if a resistor of resistance r is inserted between points $a$ and $b$ of Figure 27.39 (attached figure), the current throug it is given by

$i = \frac{E(R_s - R_x)}{(R+2r)(R_s+R_x)+2R_sR_x}$

where $E$ is e.m.f. of the ideal battery and $R=R_1=R_2$

Assume that $R_0=0$

#### Pmb

PHF Hall of Fame
I need help to solve this problem. Can anyone help me to solve this exercise? I can not really solve it. The source is Halliday.

Prove that if a resistor of resistance r is inserted between points $a$ and $b$ of Figure 27.39 (attached figure), the current throug it is given by

$i = \frac{E(R_s - R_x)}{(R+2r)(R_s+R_x)+2R_sR_x}$

where $E$ is e.m.f. of the ideal battery and $R=R_1=R_2$

Assume that $R_0=0$
The rules of this forum only allow us to help you once you've shown what you've done so far or to give you a nudge if you're unable to get anywhere at all. The later seems to be the case here so here's a hint: Draw the circuit another way, in a way that makes it look very easy to work with. Once you've done that you can use what you already know, i.e. expressions for the resistance of resistors in and parallel and in series, to solve the problem. Take it step by step.

• 1 person

#### topsquark

Forum Staff
I need help to solve this problem. Can anyone help me to solve this exercise? I can not really solve it. The source is Halliday.

Prove that if a resistor of resistance r is inserted between points $a$ and $b$ of Figure 27.39 (attached figure), the current throug it is given by

$i = \frac{E(R_s - R_x)}{(R+2r)(R_s+R_x)+2R_sR_x}$

where $E$ is e.m.f. of the ideal battery and $R=R_1=R_2$

Assume that $R_0=0$
This circuit is called a "Weatstone bridge." You might find this link to be helpful.

-Dan

#### studiot

One of the reasons for asking for information about your thoughts, besides the rules, is that there are several ways to solve this circuit.

I would not want to ofer a method that you have not (yet) been introduced to as that would just cause confusion.

At this moment we don't know what methods you have been taught so even just saying

Could I use parallel circuits, or perhaops Kirchoff's laws, but I can't see how to apply them?

would be helpful in this respect.

Here is a hint.

Label the other two corners c and d.

What do you know about the voltages at c and d?

• 1 person