Calculate the resistance to add in parallel to balance this bridge circuit

[Saibot]

Homework Statement

Find resistance R if the voltmeter reading is zero in the circuit below.

Relevant Equations

V = IRtotal, 1/R = 1/R1 + 1/R2

The reading on the voltmeter is 0.

I figure the potential drop through line AB must be the same as the potential drop through AC (since voltmeter is zero). As such, the 10 Ohm resistor has the same as the effective resistance of the parallel branch.

1/10 = 1/8 + 1/R
1/R = -0.025
R = -40 Ohms

This is clearly wrong. Help please!

 

[erobz]

Homework Statement: Find resistance R if the voltmeter reading is zero in the circuit below.
Relevant Equations: V = IRtotal, 1/R = 1/R1 + 1/R2

The reading on the voltmeter is 0.
View attachment 337192

I figure the potential drop through line AB must be the same as the potential drop through AC (since voltmeter is zero). As such, the 10 Ohm resistor has the same as the effective resistance of the parallel branch.

1/10 = 1/8 + 1/R
1/R = -0.025
R = -40 Ohms

This is clearly wrong. Help please!

I don't know if there is a trick to this, it is true that the voltage drop from AB is the same as AC. There must be different currents the branches though. So they don't have the same effective resistance as far as I can tell.

I'm having some trouble finding enough equations, ( I'm getting 2 equations in 3 unknows), but maybe I'm missing it.

 

[kuruman]

If the voltmeter reads zero, it means that the potential difference between C and B is zero. If you replace the voltmeter with a resistor, there will be no current through it. It follows that whatever current goes through the 2 Ω resistor must go through the parallel combination. Likewise, whatever current gos through the 5 Ω resistor must go through the 10 Ω resistor. What does this suggest to you? Write some equations down involving the two currents that I mentioned.

 

[erobz]

If the voltmeter reads zero, it means that the potential difference between C and B is zero. If you replace the voltmeter with a resistor, there will be no current through it. It follows that whatever current goes through the 2 Ω resistor must go through the parallel combination. Likewise, whatever current gos through the 5 Ω resistor must go through the 10 Ω resistor. What does this suggest to you? Write some equations down involving the two currents that I mentioned.

Is the total voltage source supposed to be known, and just not shown in the diagram? I really can't find that 3rd independent equation. It seems to me that something is missing...the entire circuit could very well be at zero volts (no current flowing in either branch), and the voltmeter would be none the wiser.

 

[haruspex]

Is the total voltage source supposed to be known, and just not shown in the diagram? I really can't find that 3rd independent equation. It seems to me that something is missing...the entire circuit could very well be at zero volts (no current flowing in either branch), and the voltmeter would be none the wiser.

You do have to assume that a nonzero p.d. is supplied by the accumulators.

 

[Saibot]

If the voltmeter reads zero, it means that the potential difference between C and B is zero. If you replace the voltmeter with a resistor, there will be no current through it. It follows that whatever current goes through the 2 Ω resistor must go through the parallel combination. Likewise, whatever current gos through the 5 Ω resistor must go through the 10 Ω resistor. What does this suggest to you? Write some equations down involving the two currents that I mentioned.

Got it, thank you. The current through the top is larger than the current through the bottom. Man, it seems so obvious now.

 

[Saibot]

Thanks for your input everyone!