# Using Kirchoff's Laws to solve a circuit

• lylos
In summary, for the given circuit, the current can be expressed as i = i1 + i2, where i1 = [V/(r+R)](1-e^-(t/rC)) and i2 = (V/r)e^-(t/rC). The voltage across the capacitor can be calculated using Kirchoff's law and the transient current can be obtained by calculating the voltage across the resistor.
lylos

## Homework Statement

Find i, i1, i2 in terms of V, r, R, c, and t on the following circuit:

## Homework Equations

I suppose I would use Kirchoff's law for this...

## The Attempt at a Solution

i = i1 + i2
-ir + V – i1R = 0
-ir + V – Vc = 0

Vc = V – ir = q/c
i1R = -ir + V

Where do I go from here?

Following the path with just the resistor and the capacitor can I reduce the current to the equation: i2 = (V/r)e^(-t/rC)

After the transient current that charges the capacitor has gone, you have 2 resistors in series so

V = i ( r + R)

You can get the transient by calculating the voltage across R.

This is what I'm currently thinking...

i= [V/(r+R)](1-e^-(t/rC))+(V/r)e^-(t/rC)
i1= [V/(r+R)](1-e^-(t/rC))
i2= (V/r)e^-(t/rC)

## 1. What are Kirchoff's Laws?

Kirchoff's Laws are two fundamental principles in circuit analysis that help us understand the flow of current and voltage in a circuit. They are the Kirchoff's Current Law (KCL) and the Kirchoff's Voltage Law (KVL).

## 2. How do Kirchoff's Laws help in solving circuits?

Kirchoff's Laws provide a systematic and mathematical approach to analyze complex circuits. They help us determine the unknown voltages and currents in a circuit by applying the principles of conservation of charge and energy.

## 3. What is Kirchoff's Current Law (KCL)?

Kirchoff's Current Law states that the algebraic sum of currents entering and leaving a node (or junction) in a circuit must be equal to zero. This is based on the principle of conservation of charge, where charge cannot be created or destroyed in a circuit.

## 4. What is Kirchoff's Voltage Law (KVL)?

Kirchoff's Voltage Law states that the algebraic sum of voltages around a closed loop in a circuit must be equal to zero. This is based on the principle of conservation of energy, where energy cannot be created or destroyed in a circuit.

## 5. How do we apply Kirchoff's Laws to solve a circuit?

To solve a circuit using Kirchoff's Laws, we first identify the unknown voltages and currents, then apply KCL and KVL to create a set of equations. We then solve these equations simultaneously to determine the unknown values. It is important to correctly label the currents and voltages in the circuit and correctly apply the signs (+/-) in the equations.

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