Circuit Solving Techniques:

Ohm's Law.

Kirchoff's Voltage Law.

Kirchoff's Current Law.

Nodal Analysis.

Mesh or Loop Analysis.

Linearity.

Superposition Theorem.

Theorem.

Norton's Theorm.

Ohm's Law:

Ohm's law state that the voltage across a resistor is directly proportional to the current flowing through it, when temperature is constant and source limitation is not exceeded.

v ∞ I

v = IR

Here R is constant of proportionality, is called the resistance of the conductor.

For Example:

In this diagram the value of current and resistance is given so we can easily find out the value of applied voltage by using ohm's law.

v = IR

v = ( 3mA ) × ( 6kΩ )= 18v

As we see in this diagram the value of voltage and resistance is given, the value of current is obtained when divide voltage by resistance.

I = V/R

I = 12v/6kΩ = 2mA

Solving Circuits using Ohm's Law:

Series Circuits:

In Series Circuits the value of current is remains the same .

The Value Of Voltage drops across each resistor changes, depends on the vale of the resistance .

In Series Circuits to find the value of Resistance Equivalence we add the values of each resistor.

when we break a circuit and connect a Ammeter at any point in series circuit we will see that the value of current remains the same and when we connect a Voltmeter across each resistor one by one we will see that the value of voltage drops across each resistor is different.

Circuit 1:

In this circuit there are three resistors in series with a 12v source, the value of source voltage and resistors are given.To find the value of current we solve the circuit step by step.

Step 1:

First we find Resistance Equivalence.

As resistors are in series we add the values of each resistor.

^Req.

= R1 + R2 + R3 = 6k + 4k + 2k = 12k

Now the shape of circuit may like this.

Step 2:

Now by using simple ohm's Law we can find the value of current.

I = V/R

I = ( 24v ) / ( 12kΩ )= 2mA

Parallel Circuits:

In Parallel Circuits the value of Voltage is remains the same but the value of current across each resistor is changes.

In Parallel Circuits to find the value of Resistance Equivalence we use Reciprocal formula

^1/Req

= 1/R1 + 1/R2 + 1/R3

.

Circuit 2:

case 1:

If circuit in this shape, we know that across each resistor voltage remains the same we can easily use Ohm's law to find the value of ^Io

^Io

= 12v / 2kΩ = 6mA

case 2:

But in this case if we want to find the value of " I " we first need to find the value of Resistance Equivalence.

^1/Req

= 1/2k + 1/2k + 1/3k = 8/6 kΩ

This value is obtained by using Reciprocal formula but we need the value of ^Req.

^Req

= 6/8 kΩ

Now we can use Ohm's Law to find the value of " I " .

I = ( 12v ) / ( 0.75kΩ )= 16mA

Special Case:

If there are only two resistors in Parallel circuit and we want to find the value of resistance equivalence then we use the following Rule.

^Req

=( R1 * R2 ) /( R1 + R2 )

The answer will be same either we use this Rule or by using resiprocal formula to find the value of resistance equivalence.

Kirchoff's Voltage Law.

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Kirchoff's Current Law.

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Nodal Analysis.

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Mesh or Loop Analysis.

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Linearity.

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Superposition Theorem.

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Thevenin Theorem.

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Norton's Theorm.

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