# LAB REPORT ON DC CIRCUITS

Objectives

• To build basic circuit topologies from circuit diagrams.
• To used Ohm’s law to analyze simple circuits.
• To test the theorem that any resistive Dc circuit can be reduced to a voltage source and an equivalent resistance.

Abstract

1. The lines in a circuit diagram are ignored because the distance between conductors of transmission lines is big. Thus, the inductivity is big making the R/X ratio small.
2. When resistance is added to the circuit it does not affect the voltage of the battery rather it affects the voltage distributed through the entire circuit.
• In series circuits the charge has only one path thus current is the same through all resistors since voltage is proportional to the current. On the other hand in parallel the charge has a choice but the sum of the charge flowing in each resistor should be equal to the total current. Voltage in this case is the same.

Equipment

The equipment used in this lab simulation were:

• 10V battery (resistance neglected).
• Wires with very little resistance.
• Switch(0)
• 4 resistors(27,48.5,69.5,78)

Data

Resistors in series

 Resistors R1 and R2 R1,R2 and R3 R1,R2,R3 and R4 Current A 0.13 A 0.07 A 0.04 A Voltage V 3.55V and 6.38 V 1.86v,3.38v and 4.86v 1.21v,2.16,3.10, 3.49

As seen from the data gathered from the simulation, when the resistors are in series the current through the circuit remains the same and the voltage changes in each resistor.

Resistors in parallel Data table

 Resitors R1 and R2 R1,R2,R3 R1,R2,R3,R4 Voltage v 10 v 10 v 10 v Current A 0.35, 0.20 0.35,0.20, 0.13 0.35,0.20,0.13,0.12 Total current 0.57 0.7 0.82

From the data gathered in the parallel circuit, Voltage remained the same throughout the simulation, only the current changed as the resistors were being added

Analysis

Procedure 1, series Circuits

Equivalent resistance in series = R1+R2…..R4

Calculation for Equivalent resistance for R1 and R2

Equivalent resistance (series) = R1+R2

27+48.5 = 75.5Ω

Calculation for Equivalent resistance for R1, R2 and R3

27+48.5+69.5= 145Ω

Calculation for Equivalent resistance for R1, R2, R3 and R4

27+48.5+69.5+78= 223Ω

Procedure 2, Parallel Circuits

Equivalent resistance in parallel = 1/R1 + 1/R2….R4

Calculation for equivalent resistance for R1 and R2

1/27 + 1/48.5= 0.06 Ω

Calculation for equivalent resistance for R1, R2 and R3

1/27+1/48.5+1/69.5= 0.07Ω

Calculation for equivalent resistance for R1,R2, R3 and R4

1/27+1/48.5+1/69.5+1/78= 0.08Ω

Procedure 3, Series- Parallel Circuits

• The circuit was built with a 6v battery and the resistor arranged as shown in the figure below.
• The equivalent resistance was calculated and recorded.

Equivalent resistance= R1+R2+R4+1/R3

27+48.5+78+1/69.5 =153.51Ω

The three resistors, R1,R2 and R4 are in series while R3 is parallel to the rest.

Procedure 4 series-Circuits

• The circuit was built with 6V battery and arranged as shown in the figure below.
• The current was measured and recorded.
• The equivalent resistance was later calculated.

Calculations

Equivalent resistance= 1/(R1+R3+R4)+1/R2

E= 1/174.5 +1/48.5= 0.026Ω

Conclusion

The experimental simulation was a success, the data measured were to near perfect to the calculated data using Ohm’s law. In the series circuit the current always remained the same in each resistor. Addition of a resistor the circuit reduces the current flowing in the circuit but it is evenly distributed to each resistor. In series the resistance is added directly as the current is the same and only voltage varies thus:

V= IR

Vtotal= V1+ V2+V3…..

IRT= IR1+IR2+IR3…..

Current is equal so;

I(R)= I(R1+R2+R3…), current cancels out.

RT= R1+R2+R3…..

On the other hand, in a parallel circuit, the voltage is the same and the current varies in each resistor. Addition of another resistor will increase the total current in the circuit. Also, addition of a resistor in the circuit does not affect the current in individual resistors unlike in the series circuit. Calculating resistance in a parallel circuit is done by adding the reciprocals of the individual resistors. This formula works because the voltage in the circuit is the same and only the current changes.

Itotal = I1+I2+I3….

I= V/R

V/Rt = V (1/R1+1/R2+1/R3) ….. V cancels out.

1/Rt = 1/R1+1/R2+1/R3……

For the last simulation the equivalence resistance was calculated by determining the resistors in series and the ones in parallel. Afterwards the formulas derived above were used to determine the Equivalent resistance of the circuit.

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