How to solve a circuit

 If you follow the procedure solving a circuit it will be easy. Follow below steps solving electrical circuits.

Step 1: Define the problem.

Step 2: Present everything what you know about that circuit.

Step 3: Think how many alternative solution can be possible. Pick one which is the easiest and give correct answer.

Step 4:  Try a problem solution.

Step 5: Evaluating solution and checking accuracy.

Step 6: Ask your self has the problem been solved or not? If not solved then apply step 3 again.

1. First step is the foundation of all steps. So it is most important step. Understand the problem. Spend time to clearly understand. Concentrating the problem what is asking there.
2. In second step write down everything you know. Write possible solutions. This step will save your time.
3. Third step to establish a set of alternative solutions. Chose a method of them. After understanding the circuit you have to decide how you solve the circuit by which method. So you must have knowledge about different method of circuit analysis like nodal analysis, mesh analysis etc.
4. Forth step is try a problem solution. Actually this step begins to solve.
5. Fifth step evaluate the solution. Solve with equations and check accuracy.
6. Sixth step is final. Ask yourself the problem solution is satisfactory or not? If satisfactory then perfect, if not you have to go on step 3 again to find alternative method.

Following above steps you can solve a circuit perfectly.

Now let’s solve a circuit according to these steps.

Problem: Find the current through the 16Ω resistor.

Step 1:  Define the problem carefully. We can see that there are two voltage source in this circuit. 6V source have no polarity given. So we can solve the circuit taking plus on the top of this voltage source or minus on the top both ways if we have enough time. If we have no enough time them we chose one way. Here I am have chosen minus at the top. Hence the circuit becomes as below.

Step 2: Present everything you know the circuit. There are three resistors given with values. Here asking to find the current through 16Ω resistor.

Step 3: Establishing a set of alternative solutions here in this steps. Ask yourself which techniques can be applied to solve the circuit. You can solve this circuit using three techniques are nodal analysis, mesh analysis and using KVL-KCL. I have chosen nodal analysis method because if I use mesh analysis there will be written many equation to solve. If you have no idea about nodal analysis read nodal analysis method by clicking here. This is the easiest approach here.

Using nodal analysis the circuit becomes as below

Step 4: Attempt a problem solution. We have to find out current through 16Ω resistors. According to nodal analysis we get equations,

              (v₁ – 10)/ 4 + (v₁ – 0)/ 16 + (v₁ + 6)/ 8 = 0

         Or,  7v₁ = 28

          v₁ = 4V

We get,  (v₁ – 0) = i_16Ω R_16Ω

So  i_16Ω = (v₁ – 0) / R_16Ω = 4/16 = 0.25A

 i_16Ω = 0.25A

Step 5: checking for accuracy. Applying KVL,

 i₁ = (v₁ – 10)/ 4 = (4 – 10)/4 = -1.5 A

 i₂ = (v₁ + 6)/ 8 = (4 + 6)/ 8 = 1.25A

i_16Ω = 0.25A

According to KCL,    i₁ +  i₂ + i_16Ω = -1.5 A + 1.25A + 0.25A = 0.

As it is obeyed KCL so it is checked perfectly.

Applying KVL loop 1,

-10 + v_4Ω + v_16Ω = -10 + {- (-1.5*4)} + 0.25*16

                           =  0 (checked)

Applying KVL loop 2,

– v_16Ω + v_8Ω – 6 = – 0.25*16 + 1.25*8 – 6

                         = 0  (checked)

So we can say that the answers are accurate.

Step 6:  Has the problem been solved with satisfactory? Yes our problem is solved satisfactory. If your answer is not satisfactory then go back step 3 and do again.