Superposition Theorem 1w604n

Objectives 1. To understand the concept of superposition theorem. 2. To be able to cope with more than one voltage source in a circuit. 3. To identify a linear circuit. List of Instruments 1 piece VOM 1 set electronics trainer () 1 piece milliammeter (DC) Wiring Diagram A) Linearity R 1=

1

K

R

V

2

=

4

7

0

R

3

=

6

8

0

s

B) Superposition R 1=

1

K

R

1

5

V

2

=

4

5

7

0

V

R

3

=

6

8

0

Data Sheet A) Source 5 10 15

V1 (volts) 4.07 8.06 12.12

I1 (mA) 4 8 12

B) Measured values

15 V ON ON OFF

Calculated values

5V ON OFF ON

V1 10.58 12.02 1.418

V2 4.33 2.894 1.425

V3 -0.7 2.894 -3.55

I1 10.5 12 -1.4

I2 11.5 7.7 3.8

I3 -1 4.2 -5.2

10.602

4.319

-0.656

10.6

11.5

-1

Problem and Solution V1 = V1’ + V1’’ = 12.02 – 1.418 = 10.602 V V2 = V2’ + V2’’ = 2.894 + 1.425 = 4.319 V V3 = V3’ + V3’’ = 2.894 – 3.55 = -0.656 V I1 = I1’ + I1’’ = 12 – 1.4 = 10.60 mA I2 = I2’ + I2’’ = 7.7 + 3.8 = 11.5 mA I3 = I3’ + I3’’ = 4.2 – 5.2 = -1 mA Analysis We can say that the relationship between current (input) and voltage (output) is linear for a resistor when it satisfies the following conditions: (1) the response to a sum of inputs is equal to the sum of the individual responses (output). (2) If the excitation is scaled by the constant K in “R(Ki) = K(Ri) = Kv’, then the response is also scaled by K. The algebraic sum of voltages or current caused by each independent source acting alone is equal to the total voltage or current caused by all sources acting together. This law had been proven for the second circuit with an infinitesimal change in values.

Conclusion By also using an alternative Ohm’s law (I = V/R), we can show that the relationship between voltage (excitation) and current (response) is also linear for a resistor. The concept, known as the principle of superposition is a direct consequence of the linearity property of circuits.