Kirchhoff's Rules Homework: Rewrite for Disconnected Circuit

[Midgela25]

Homework Statement

The question shows a picture of a general circuit containing two power supplies and three resistors. The equation V=(3R/2)I subscript 3 explains Kirchhoffs Rules. The question asks to rewrite Kirchhoff's rules for the circuit if the power supply with voltage V subscript 2 and the resistor with the resistance R subscript 2 are disconnected from the circuit.


Relevant equations[/b]

Kirchhoffs Rules : V= (3r/2) I subscript 3

The Attempt at a Solution

My attempt to the solution would be V=(2R)I subscript 3.
Any help would be greatly appreciated. I attached a picture of what the circuit looks like. Any help would be greatly appreciated. Thanks

 

[anathema]

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Thank you for your question. Based on the information provided, it seems that the circuit you are dealing with is a combination of series and parallel connections. In order to properly rewrite Kirchhoff's rules for this circuit, we will need to consider the effects of both series and parallel connections.

First, let's review Kirchhoff's rules. The first rule, also known as Kirchhoff's current law, states that the sum of all currents entering and leaving a node in a circuit must equal zero. This means that the current entering the node is equal to the current leaving the node. The second rule, also known as Kirchhoff's voltage law, states that the sum of all voltages around a closed loop in a circuit must equal zero. This means that the voltage drops across all components in the loop must equal the voltage rise from the power supply in the loop.

Now, let's consider the circuit with the disconnected power supply and resistor. Since the power supply and resistor are no longer in the circuit, we can simplify the circuit to only include the remaining power supply, resistor, and the two remaining resistors. This simplified circuit can be analyzed using Kirchhoff's rules to determine the new voltage and current values.

For Kirchhoff's current law, we can see that the current entering the node where the two remaining resistors are connected must equal the current leaving the node. This means that the current through the two remaining resistors, I subscript 3, must equal the current through the remaining power supply and resistor, I subscript 2. Therefore, we can rewrite Kirchhoff's first rule for this simplified circuit as: I subscript 3 = I subscript 2.

For Kirchhoff's voltage law, we can see that there is now only one closed loop in the circuit, which includes the remaining power supply, resistor, and the two remaining resistors. This means that the voltage drops across all components in this loop must equal the voltage rise from the power supply. We can express this using the following equation: V subscript 2 + (3R/2)I subscript 3 = V subscript 1. This is because the voltage drop across the two remaining resistors is equal to (3R/2)I subscript 3, and the voltage drop across the remaining power supply and resistor is equal to V subscript 2.

Now, we can substitute the value of I subscript 3 from Kirchhoff

 

[nlightner]

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Kirchhoff's Rules are fundamental principles in circuit analysis that help us understand and solve complex circuits. In the given circuit, we have two power supplies and three resistors. The equation V=(3R/2)I subscript 3 represents the voltage drop across resistor 3, as determined by Kirchhoff's Voltage Law (KVL). However, if we disconnect the power supply V subscript 2 and resistor R subscript 2 from the circuit, the equation would change to V=(2R)I subscript 3. This is because without the contribution of V subscript 2 and R subscript 2, the voltage drop across resistor 3 would only be determined by the remaining power supply and resistor in the circuit. Therefore, the new equation reflects the updated circuit with the disconnected components. It is important to note that Kirchhoff's Rules are still applicable even in a disconnected circuit, as they are fundamental principles that hold true in all circuits.