Kirchhoff's Rules. Solving for currents in circuit with two batteries

• Painguy
In summary, the problem involves determining the currents through resistors R2 and R3, each with a resistance of 4.0 Ω, in a circuit with two batteries (5V and 10V). Superposition can be used to solve for the currents by considering each battery separately and then adding the results.
Painguy

Homework Statement

What are the sizes and directions of the currents through
resistors (a) R2 and (b) R3 in Fig. 27-42, where each of the three resistances is 4.0 Ω?

ΔV=IR

The Attempt at a Solution

Equations:
1) ΔVB2 -(i1)R1 -(i2)R2 -ΔVB1=0
5V - 4(i1) - 4(i2) =0
4(i2)=5V -4(i1)

2) ΔVB2 -(i1)R1 -(i3)(R3)=0
10V -4(i1) -4(i3) =0
-4(i3)=-10V + 4(i1)

3) ΔVB1 -(i2)R2 -(i3)(R3)=0
5V + 4(i2) -4(i3) =0

4) i1=i2 + i3

5V +5V -4(i1) -10V +4(i1)=0
0=0

I'm not really sure what to do here.

Last edited:
Painguy said:

Homework Statement

What are the sizes and directions of the currents through
resistors (a) R2 and (b) R3 in Fig. 27-42, where each of the three resistances is 4.0 Ω?

ΔV=IR

The Attempt at a Solution

Equations:
1) ΔVB2 -(i1)R1 -(i2)R2 -ΔVB1=0
5V - 4(i1) - 4(i2) =0
4(i2)=5V -4(i1)

2) ΔVB2 -(i1)R1 -(i3)(R3)=0
10V -4(i1) -4(i3) =0
-4(i3)=-10V + 4(i1)

3) ΔVB1 -(i2)R2 -(i3)(R3)=0
5V + 4(i2) -4(i3) =0

4) i1=i2 + i3

[STRIKE]5V +5V -4(i1) -10V +4(i1)=0
0=0[/STRIKE]

I'm not really sure what to do here.

The blue equation is not independent from the previous ones. Use eq.4 to find i1.

ehild

I also suggest superposition:
solve for the currents with one battery shorted, solve with the other battery shorted, then add the results.

1. What are Kirchhoff's Rules?

Kirchhoff's Rules, also known as Kirchhoff's Circuit Laws, are a set of fundamental principles used to analyze electric circuits. These rules, developed by German physicist Gustav Kirchhoff in the mid-19th century, are used to determine the voltage, current, and resistance at various points in a circuit.

2. What is the first rule of Kirchhoff's Rules?

The first rule, known as Kirchhoff's Current Law (KCL), states that the sum of currents entering a junction in a circuit must be equal to the sum of currents leaving that junction. This is based on the principle of conservation of charge, which states that charge cannot be created or destroyed in a closed circuit.

3. What is the second rule of Kirchhoff's Rules?

The second rule, known as Kirchhoff's Voltage Law (KVL), states that the sum of voltage drops in a closed loop must be equal to the sum of voltage rises. This is based on the principle of conservation of energy, which states that energy cannot be created or destroyed in a closed circuit.

4. How do Kirchhoff's Rules help solve for currents in a circuit?

By applying Kirchhoff's Rules, we can create a system of equations that can be solved to determine the unknown currents in a circuit. KCL can be used to determine the currents at junctions in the circuit, while KVL can be used to determine the voltages across various components in the circuit.

5. Can Kirchhoff's Rules be used in circuits with multiple batteries?

Yes, Kirchhoff's Rules can be applied to circuits with multiple batteries. KVL can be used to determine the voltage drops across each battery, and KCL can be used to determine the currents at junctions in the circuit. It is important to consider the direction of current flow and voltage polarity when applying these rules in circuits with multiple batteries.

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