Calculate Current Through Resistor - Kirchhoff's Rules

In summary, the conversation is about calculating the current through a resistor in circuit B using Kirchhoff's loop and junction rules. The equations for the two loops and the fact that I1 = I2 were provided. The final equation for I3, which is (2EMF) / (R1 +2R2), was obtained by eliminating I1 (or I2) from the first two equations and expressing it in terms of I3. The solution requires substitution and rearranging of equations.
  • #1
crimsonn
30
0

Homework Statement


Calculate the current through the resistor of resistance for circuit B.

Express your answer in terms of EMF, R1, and R2.

http://imageshack.us/photo/my-images/163/screenshot20111112at110.png/"

Homework Equations



Kirchhoff's Loop and junction rules

The Attempt at a Solution


So I have these equations that I've figured out using Kirchhoff's Rules:

There are two loops:

EMF = I1R1 + I3R2
EMF = I2R1 + I3R2
I1 + I2 = I3

I figured out pretty quickly that I1 = I2 by subtracting the top from the middle equation. I'm just not sure what to do next really...

The answer I'm supposed to get to is I3 = (2EMF) / (R1 +2R2)

I don't know why this is so confusing...but it is. So, assuming I did everything right, how do I get to the last (final) equation for I3?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
crimsonn said:
I figured out pretty quickly that I1 = I2 by subtracting the top from the middle equation. I'm just not sure what to do next really...
Make use of that fact to eliminate I1 (or I2) from either of the first two equations. Express I1 (or I2) in terms of I3. (Use your third equation.)
 
  • #3
Simply use more substitution and rearranging to get the equation you want. You already have all the equations necessary, you don't even have to think about it anymore, just write out your equations (including your equation I1=I2), and then its just a problem of simultaneous equation solving.
 
  • #4
I think I'm super sleep deprived because that was pretty simple.

Thanks you two :)
 
  • #5


To solve for I3, you can use substitution to eliminate I1 and I2 from the equations. From the first two equations, we have:

I1 = (EMF - I3R2) / R1
I2 = (EMF - I3R2) / R1

Substituting these into the third equation, we get:

(EMF - I3R2) / R1 + (EMF - I3R2) / R2 = I3

Multiplying both sides by R1R2, we get:

R2(EMF - I3R2) + R1(EMF - I3R2) = R1R2I3

Expanding and rearranging, we get:

2EMF - 2I3R2 = R1R2I3

Solving for I3, we get:

I3 = (2EMF) / (R1 + 2R2)

Therefore, the current through the resistor in circuit B is (2EMF) / (R1 + 2R2).
 

Related to Calculate Current Through Resistor - Kirchhoff's Rules

1. How do Kirchhoff's Rules apply to calculating current through a resistor?

Kirchhoff's Rules, specifically the Junction Rule and Loop Rule, can be used to calculate the current through a resistor in a circuit. The Junction Rule states that the sum of the currents entering a junction must equal the sum of the currents leaving the junction. The Loop Rule states that the sum of the voltage drops in a closed loop must equal the sum of the voltage sources in that loop.

2. What is the formula for calculating current through a resistor using Kirchhoff's Rules?

The formula for calculating current through a resistor using Kirchhoff's Rules is I = V/R, where I is the current through the resistor, V is the voltage drop across the resistor, and R is the resistance of the resistor. This formula can be derived by applying the Loop Rule and Ohm's Law.

3. Can Kirchhoff's Rules be used for both series and parallel circuits?

Yes, Kirchhoff's Rules can be used for both series and parallel circuits. In a series circuit, the Junction Rule can be used to calculate the current through each resistor, and the Loop Rule can be used to calculate the total voltage drop. In a parallel circuit, the Junction Rule can be used to calculate the total current entering and leaving each junction, and the Loop Rule can be used to calculate the voltage drop across each resistor.

4. How do I know which direction to assign for current flow when using Kirchhoff's Rules?

When using Kirchhoff's Rules, the direction of current flow is typically assigned arbitrarily. However, it is important to be consistent with the assigned direction throughout the calculation. If the calculated current is negative, it simply means that the actual direction of current flow is opposite to the assigned direction.

5. Are there any limitations to using Kirchhoff's Rules to calculate current through a resistor?

Kirchhoff's Rules are based on the principles of conservation of charge and energy, and are applicable to all types of circuits. However, these rules assume ideal conditions and do not take into account factors such as resistance of wires and non-ideal behavior of components, which may affect the accuracy of the calculated current through a resistor in a circuit.

Similar threads

Kirchhoff's law: Find the current I3 through the Amp meter
    • Introductory Physics Homework Help
Replies
4
Views
949
How to solve this chain with Kirchhoff's laws?
    • Introductory Physics Homework Help
Replies
18
Views
2K
Power dissipated in this circuit with 2 batteries and 3 resistors
    • Introductory Physics Homework Help
Replies
22
Views
3K
Two batteries and two resistors circuit - wrong possible answers ?
    • Introductory Physics Homework Help
Replies
16
Views
1K
Why Are My Kirchhoff Voltage Rule Equations Incorrect?
    • Introductory Physics Homework Help
Replies
1
Views
791
Finding the currents in this circuit (2 voltage sources and 3 resistors)
    • Introductory Physics Homework Help
Replies
10
Views
2K
Solving Kirchoff's Laws: Are My Answers Correct?
    • Introductory Physics Homework Help
Replies
9
Views
2K
How does induced current change when a loop accelerates through a magnetic field?
    • Introductory Physics Homework Help
Replies
8
Views
709
Calculate Currents Through Ideal Batteries with Kirchhoff's Loop Rule
    • Introductory Physics Homework Help
Replies
5
Views
2K
Using Kirchhoff's laws on this current division problem
    • Introductory Physics Homework Help
Replies
12
Views
1K

Hot Threads

Recent Insights

Back
Top