Potential difference between two points on a circuit

[terryds]

Homework Statement

The circuit is shown as above.
If ε = 3 volt and each resistor has 2 ohm resistance, then what's the potential difference between point B and point D ?

A. 4
B. 3
C. 2
D. 1
E. 0

Homework Equations

V = I R
R series = R1 + R2 + ..
1/ R parallel = 1/R1 + 1/R2 + ...

The Attempt at a Solution

[/B]
The circuit is very weird. I don't even know how to start.

 

[cnh1995]

Are you familiar with Kirchhoff's laws?

 

[terryds]

Are you familiar with Kirchhoff's laws?

Yes, of course.. KVL and KCL..
Okay, I'll use KVL for the two triangles

Triangle ADC

4IR = ε
I = ε/4R = 3/8 ampere

The current in triangle ABC also 3/8 ampere, right ? (The resistance are equal also the emf)

But, what's the potential difference between point B and D?

 

[cnh1995]

Assume current through diagonal AC as i and current through ABC as i₁. So, current through ADC is i-i1. Using these currents, write KVL and you'll get values for i and i1.
Actually, this problem can be solved by observation only, using the symmetry of the circuit.

 

[terryds]

Assume current through diagonal AC as i and current through ABC as i₁. So, current through ADC is i-i1. Using these currents, write KVL and you'll get values for i and i1.

$Triangle\ ABC \\ 2I_1R+2IR - \varepsilon = 0 \\ 4I_1 + 4I = 3\\ Triangle\ ADC \\ 2((I-I_1)R) + 2IR - \varepsilon = 0 \\ 4IR-2I_1R = 3 \\ 8I - 4I_1 = 3 \\$

Solving the equation, I get i = 0.5 A, and i1 = 0.25 A, and it means that i2 = 0.25 A
How to determine the potential difference between B and D ??

Actually, this problem can be solved by observation only, using yhe symmetry of the circuit.

Yeah, I also see that it's kinda like the Wheatstone bridge, isn't it ??
But, eventually, the current through diagonal AC is not zero (not as I thought it would be in Wheatstone bridge)..
Please help me

 

[cnh1995]

Solving the equation, I get i = 0.5 A, and i1 = 0.25 A, and it means that i2 = 0.25 A

Good!

How to determine the potential difference between B and D ??

Let's say point A is at a potential V_a and point B is at potential V_b. Voltage drop across the resistor between A and B is Va-Vb. What is the value of this voltage drop? You know the currents now.

 

[terryds]

Good!

Let's say point A is at a potential V_a. You know the currents now. What is the potential of point B in terms of V_a and known current and resistor values? (Hint:Ohm's law).

Vb = 3 - 0.5 * 2 - 0.25 * 2 = 1.5 V
Vd = 3 - 0.5 * 2 - 0.25 *2 = 1.5 V
The potential difference is zero, right ?

Anyway, is this circuit a Wheatstone bridge?

 

[cnh1995]

The potential difference is zero, right ?

Right.

Anyway, is this circuit a Wheatstone bridge?

Yes. Supply is connected between A and C and output is taken between B and D.