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Computer science.B.tech in CSE

1. KVL Derive equivalent resistance when connected in series   Presented by:- Rudra prasad Baral Regd no:- 220301120187 SEC:- C

2. content KVL introduction Properties Equivalent resistance in series circuit Conclusion 2

3. Kirchhoff's Voltage Law, or KVL, is a fundamental principle in electrical engineering that states that the sum of all voltages around any closed loop in a circuit must equal zero. This law is based on the conservation of energy and is essential for analyzing complex circuits with multiple loops and branches . 3 KVL

4. Continued Below is a single loop circuit. The KVL computation is expressed graphically in that voltages around a loop are summed up by traversing the loop. 4

5. Properties In KVL sign convention is most important. The loop must start and end at the same point. It does not matter where you start on the loop. If a circuit has multiple loops, Kirchhoff’s Voltage law is true for every loop. We can go around the loop in either direction, clockwise or anticlockwise. Kirchhoff’s law still holds. 5

6. Example 6 Step 1 – Assign Loop name: Step 2 – Assign Sign to circuit elements Step 3 – Assign current names At node a: I1 = I1 At node b: I1 = I2+I3 At node c: I2+I3 = I1 Write node equa tions For loop1 : V = I1R1 + I2R4 For loop2: 0 = I3R2 + I3R3 – I2R4

7. Equivalent resistance in Series circuit 7 In an electrical circuit, the total resistance of a series circuit can be calculated by adding up the individual resistances of each component. When resistors are connected in series, the current flowing through each resistor is the same. The voltage across each resistor, however, is different and can be calculated using Ohm's Law. The total resistance of the circuit is equal to the sum of the individual resistances.

8. Continued 8 Here is R eq = R1 + R2 + R3

9. Conclusion 9 In series circuit current is same across all the resistance. But voltage drops across each resistance is difference due to different resistance value as given by ohms law. Voltage drop are additive. Voltage are divided in series circuit, current is constant .