Determine potential difference (circuits)

[kyle]

Homework Statement

V_a - V_b

Homework Equations

V = IR
Loop rule
Node rule

The Attempt at a Solution

I'm able to find each I value, as well as the direction of current. I'm not sure what to do after that. I know the answer should be 45V, but everything I've tried doesn't lead to that.

 

[ehild]

Choose the zero of the potential at b. Knowing the currents on each resistor, choose a path leading from b to a, find the change of potential across each element. Note that the potential decreases in the direction of flow of a current.


ehild

 

[mr_pavlo]

45,3846V exactly, that is 590/13V

 

[ehild]

45,3846V exactly, that is 590/13V

It looks correct.

ehild

 

[HalfLostAndSearching]

To determine the potential difference between Va and Vb, you can use the loop rule and node rule to analyze the circuit. The loop rule states that the sum of the potential differences around a closed loop in a circuit must be equal to zero. The node rule states that the sum of the currents entering a node must be equal to the sum of the currents leaving the node.

Using these rules, you can set up equations to solve for the potential difference between Va and Vb. For example, you could start by writing the loop rule equation for the loop containing Va and Vb. This would give you an equation with the known potential differences and the unknown potential difference between Va and Vb.

Similarly, you could write the node rule equation for the node containing Va and Vb. This would give you an equation with the known currents and the unknown potential difference between Va and Vb.

You can then solve these equations simultaneously to find the potential difference between Va and Vb. In this case, the potential difference between Va and Vb should be 45V.