Circuit with Four Resistors and Two Switches

[Jake Russell]

Homework Statement

Four resistors connected to a battery are shown in the figure (at bottom). The switch S₂ is closed and switch S₂ is left open. What is the magnitude of the potential difference V_cd

Homework Equations

R_p= Σ(1/R_i)^-1

R_s = ∑R_i

V = IR

The Attempt at a Solution

Seeing as c and d aren't directly connected since S₂ is open, I attempted to find the total resistance using the two resistance equations above and from that find the total current. After that, I divided the total current by two since the total resistance on both sides are the same, and multiplied that by the total of the top resistance. Next I added the current multiplied by the bottom left resistor and subtracted the current multiplied by the bottom right resistor, but I don't think this is correct.

 

[gneill]

Hi Jake Russell, Welcome to Physics Forums!

The mage that you tried to attach isn't viewable. Can you upload it again?

 

[Jake Russell]

I ended up figuring out this question (I wasn't starting at a and not c), but I have another one. How would I find the current through the second switch when it is closed?

 

[gneill]

With switch S2 closed can you find the potential at node cd? (Since S2 joins c and d together, they become a single node).

Knowing the potentials at a,b, and c, can you write a KCL equation at location c?

 

[CWatters]

Work out the voltage drop across each resistor (easy) then calculate the current in each resistor and mark it on the diagram. Apply KCL at either node c or d.

Edit: cross posted with gneill.