Solving Kirchhoff's Rules: Electric Circuits and Algebra Practice

[teken894]

This is a problem from my physics book. We are learning Kirchhoff's rules with electric circuits and I'm at a loss at what to do here.

I apply them just fine to a three loop circuit, using some algebra:
|-/\/\-|\//\ -|
| |
|--|\--/\/\/--|
| |
|---|\--/\/\--|

Like so..where |\ is a battery and /\/\ indicate resistors. I can find the current in a similar circuit, voltage drops, etc

But this problem:
http://66.93.135.68/phy_prob.gif

I don't know where to begin..or how to apply the rules. Can someone help me in finding the terminal voltage of the batteries??

Thanks

 

[maverick280857]

I don't know where to begin..or how to apply the rules. Can someone help me in finding the terminal voltage of the batteries??
Thanks

You have to sum the drops across each circuit element. What is terminal voltage and how is it defined mathematically for an emf E with internal resistance r for which current i is flowing out of the positive terminal?

 

[kyle8921]

for sharing your problem and asking for help. Solving Kirchhoff's rules can be challenging, but with some practice and understanding of the concepts, it can become easier. Let's break down the steps to solve this problem.

First, let's label the nodes and loop currents in the circuit. Nodes are the points where two or more branches meet, and loop currents are the currents that flow through each loop in the circuit. Labeling the nodes and loop currents will help us keep track of the variables in our equations.

Next, we need to apply Kirchhoff's rules. Kirchhoff's first rule, also known as the junction rule, states that the sum of the currents entering a node is equal to the sum of the currents leaving the node. This can be written as an equation for each node in the circuit.

For node A, we have:
I1 + I2 + I3 = 0

For node B, we have:
I1 + I4 = 0

For node C, we have:
-I2 + I3 + I4 = 0

Kirchhoff's second rule, also known as the loop rule, states that the sum of the voltage drops around a closed loop in a circuit is equal to the sum of the voltage sources in that loop. This can be written as an equation for each loop in the circuit.

For the top loop, we have:
-V1 + R1*I1 + R2*(I1 - I2) = 0

For the middle loop, we have:
-V2 + R3*(I2 - I3) + R4*(I2 - I4) = 0

For the bottom loop, we have:
-V3 + R5*I3 + R6*(I3 - I4) = 0

Now we have a system of equations that we can solve using algebra to find the values of the loop currents and terminal voltages. Once we have the values for the loop currents, we can use them to find the terminal voltages of the batteries.

I hope this helps guide you in solving this problem. Remember to always label your nodes and loop currents, and apply Kirchhoff's rules to each node and loop in the circuit. With practice, you will become more comfortable with solving these types of problems.