LAWS AND THEOREMS FOR CIRCUIT SOLVING (PART 1)

Circuit solving is the most important and most difficult part of circuit analysis, if the laws to solve them are not studied properly. 

In this post, some important laws are going to be studied. Starting with voltage division rule.


VOLTAGE DIVISION RULE -

This rule can be applied when two or more resistors are connected in series. Because for parallel connections, the voltage across the entire branch in parallel remains same as the supply voltage.

Rule - To find out the voltage across a resistance (Rx), then unknown resistance divided by the total resistance of that branch, the whole multiplied by the supply voltage.

Eg 

         In the circuit shown, 

Supply voltage (V1) = 12V ,  R1 = 10K ,  R2 = 4.7K

To find voltage across R2, (Vr2)

Vr2 = [R2 / (R1 + R2)] * V1

ie Vr2 =   3.83V

Output from Multisim simulation, showing the voltage across R2

CURRENT DIVISION RULE -

This rule can be used only when two branches are in parallel, and the total current arriving at the parallel combination is known. Because, in series, the total current in the circuit remains the same.

Rule - 

To find the current flowing in an unknown resistance (Rx), the resistance of the other branch divided by the total resistance, the whole multiplied by the total current.

Eg - 

          In the  circuit shown, 

Supply voltage (V1) = 12V ,

R12 (R1 + R2) = 14.7K

R34 (R3 + R4) = 5.3K

Total resistance = 1/[(1/R12) + (1/R34)]

                          = 3.8955K

(Total current) I = V1 / Tot. resistance 

                           = 12 / 3.8955 = 3.08mA

I34 = [R12 / (R12 + R34)] * I =  2.2638mA

Multisim output, showing current in branch R34

KIRCHHOFF'S VOLTAGE LAW (KVL) - 

It states that, The sum of the all the potential differences in the loop is equal to zero. 

OR

The sum of the voltage drops across all the components in a loop is equivalent to the supply voltage.

Important points - 

• When moving in the loop, if, the first terminal of the device appearing is +ve, then potential difference across it is to be taken as -ve.
• If the first terminal is -ve, then voltage should be taken as +ve.

Eg - 

In the loop given, by applying the Kirchhoff's voltage law, we get  -  

VS1 - V1 - V2 + VS2 - V3 = 0 

Or 

VS1 + VS2 = V1 + V2 + V3

Kvl proof in multisim -

Adding all the voltages we get,         12 - 10.18 - 4.784 - 2.036 + 5 = 0 

Hence, proved !!!

Important point to be noted - 

• If in a same component there are two current components, then-
• Travelling from A to B ,  V(r1) = R1*(Ib - Ia)
• Travelling from B to A ,  V(r2) = R1*(Ia - Ib)

KIRCHHOFF'S CURRENT LAW (KCL) -

It states that, the sum of all the currents entering a node or a junction is equal to the sum of currents leaving the node.

Eg - 

Applying KCL to the circuit , 

I1 = I2 +I3

Proof, using Multisim simulations -

Adding the current elements using KCL,       1.052mA = 314.193uA + 738.298uA

Hence, proved !!!

Thr next post will be about, Superposition theorem, Thevenin's thm, Norton's thm.

Thank you .!!!

Corrections and suggestions welcome.