Loop Rule - Batteries and Resistors

In summary, the problem involves two batteries and three resistors connected in a circuit. The task is to determine the amount of current flowing through each battery when the switch is opened and closed. Using Kirchoff's Rule and breaking the circuit into two loops, the equations for each loop can be set up and solved to find the values of I1, I2, and I3.
  • #1
ihearyourecho
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0

Homework Statement



Two batteries and three resistors are connected as shown in the figure .
http://session.masteringphysics.com/problemAsset/1122583/1/Walker.21.52.jpg

A) How much current flows through 6.0 V battery when the switch is closed?
B) How much current flows through 9.0 V battery when the switch is closed?
C) How much current flows through 6.0 V battery when the switch is open?
D) How much current flows through 9.0 V battery when the switch is open?


Homework Equations



Kirchoff's Rule

The Attempt at a Solution



I broke it down into two different loops, the one on the left and the one on the right. I labeled the 6V battery as E1 and the 9V one as E2. I called the current flowing upward from 6V I1 and the current flowing upward from 9V I2. I labeled the resistor under the 6V battery R1 and the resistor under the 9V battery R2.

From this, here are my equations:

For Loop 1:
E1-E2-I1R1+I2R2=0

For Loop 2:
E2-I3R3-I2R2=0

Both of these due to Loop Rule.

I'm not sure where to go from here, or even if these are totally correct.

Help would be great :)
 
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  • #2
Hi ihearyourecho! :smile:

(try using the X2 tag just above the Reply box :wink:)

An equation relating I1 I2 and I3 would be pretty cool. :rolleyes:
 
  • #3
After sitting down with my teacher and getting some help from him, I was able to crank through the problem. Thanks for the tip about super and subscripts though!
 

FAQ: Loop Rule - Batteries and Resistors

What is the loop rule?

The loop rule, also known as Kirchhoff's voltage law, states that the algebraic sum of all voltages in a closed circuit is equal to zero. This means that the sum of the potential differences across each component in a circuit must equal the total voltage supplied by the battery.

How do batteries and resistors affect the loop rule?

Batteries and resistors are both components that contribute to the overall voltage in a circuit. Batteries provide a fixed voltage, while resistors create a voltage drop based on their resistance. Both of these must be taken into account when applying the loop rule.

Can the loop rule be applied to parallel circuits?

Yes, the loop rule can be applied to parallel circuits. In this case, the sum of the voltage drops across each resistor must still equal the total voltage supplied by the battery, even though the current is split between multiple paths.

What happens if the loop rule is not satisfied?

If the loop rule is not satisfied, it means that there is a violation of conservation of energy in the circuit. This usually occurs due to a mistake in the circuit design or calculations. The circuit will not function properly until the loop rule is satisfied.

Can the loop rule be used to calculate individual voltages in a circuit?

No, the loop rule can only be used to calculate the total voltage in a circuit. It cannot be used to determine the voltage across individual components. To calculate the voltage across a specific component, you would need to use Ohm's law or a voltage divider equation.

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