Lab Report 1: Ohms Law and Kirchhoff’s Law Verification

1. THEORY OF OHMS LAW AND KIRCHHOFF’S LAW

Ohms Law

It states that at constant physical conditions, the current flowing through a conductor is directly proportional to the potential difference across its ends. This is the core principle of Ohms Law.

i.e., \(V \propto I\)

\(V = IR\)

Where R is the constant of proportionality, known as resistance.

Kirchhoff’s Law

a. First Law (Kirchhoff’s Current Law – KCL): In an electric circuit, the algebraic sum of currents at any junction point is zero.

i.e., \(\Sigma I = 0\)

b. Second Law (Kirchhoff’s Voltage Law – KVL): In a closed circuit, the algebraic sum of the products of current and resistance is equal to the total EMF in the circuit.

i.e., \(\Sigma E = \Sigma IR\)

2. OBSERVATION TABLE FOR OHMS LAW

Data for Ohms Law Verification:

• Standard value of resistance (R) = 20 Ω
• Value of 1 small division of ammeter = 0.02 A
• Value of 1 small division of voltmeter = 0.02 V

a. For Ohms Law

S.N.	Voltage (V)	Current (I) in A	Resistance (R) in Ω	Mean Resistance (Rm) in Ω
1	5	0.18	27.78	25.81
2	10	0.38	26.31
3	15	0.6	25.00
4	20	0.8	25.00
5	25	1.0	25.00

b. For Kirchhoff’s Voltage Law (KVL)

S.N.	Vs (V)	V1 (V)	V2 (V)	VT = V1+V2 (V)	Current (I) in A	R = VT/I (Ω)	P = VT x I (Watt)
1	5	3.20	1.66	4.86	0.14	34.71	0.6804
2	10	6.58	3.40	9.98	0.26	38.38	2.5948
3	15	9.82	5.12	14.94	0.40	37.35	5.976

c. For Kirchhoff’s Current Law (KCL)

S.N.	Vs (V)	I1 (A)	I2 (A)	IT = I1+I2 (A)	P = V x IT (Watt)
1	5	0.38	0.22	0.60	3.0
2	10	0.72	0.34	1.06	10.6
3	15	1.08	0.60	1.68	25.2

3. CALCULATION

a. For Ohms Law

• \(R_1 = V/I = 5 / 0.18 = 27.78 \Omega\)
• \(R_2 = V/I = 10 / 0.38 = 26.31 \Omega\)
• \(R_3 = V/I = 15 / 0.6 = 25 \Omega\)
• \(R_4 = V/I = 20 / 0.8 = 25 \Omega\)
• \(R_5 = V/I = 25 / 1 = 25 \Omega\)
• Mean (Rm) = (27.78 + 26.31 + 25 + 25 + 25) / 5 = 25.81 Ω

b. For KVL

• \(V_{T1} = V_1 + V_2 = 3.2 + 1.66 = 4.86 V\)
• \(V_{T2} = V_1 + V_2 = 6.58 + 3.40 = 9.98 V\)
• \(V_{T3} = V_1 + V_2 = 9.82 + 5.12 = 14.94 V\)
• \(R_1 = V_T / I = 4.86 / 0.14 = 34.71 \Omega\)
• \(R_2 = V_T / I = 9.98 / 0.26 = 38.38 \Omega\)
• \(R_3 = V_T / I = 14.94 / 0.4 = 37.35 \Omega\)
• \(P_1 = V_T \times I = 4.86 \times 0.14 = 0.6804\) Watt
• \(P_2 = V_T \times I = 9.98 \times 0.26 = 2.5948\) Watt
• \(P_3 = V_T \times I = 14.94 \times 0.4 = 5.976\) Watt

c. For KCL

• \(I_{T1} = I_1 + I_2 = 0.38 + 0.22 = 0.6\) A
• \(I_{T2} = I_1 + I_2 = 0.72 + 0.34 = 1.06\) A
• \(I_{T3} = I_1 + I_2 = 1.08 + 0.6 = 1.68\) A
• \(P_1 = V \times I_T = 5 \times 0.6 = 3\) W
• \(P_2 = V \times I_T = 10 \times 1.06 = 10.6\) W
• \(P_3 = V \times I_T = 15 \times 1.68 = 25.2\) W

4. ERROR ANALYSIS FOR OHMS LAW

Relative error in Resistance (R) from Ohms Law:

\(= |(R_{standard} – R_{mean}) / R_{standard}| \times 100\%\)

\(= |(20 – 25.81) / 20| \times 100\% = 29.05\%\)

5. RESULT

• Resistance (R) from Ohms Law: 25.81 Ω
• KVL Verification: \(V_T = V_1 + V_2\). For instance, \(4.86V = 3.2V + 1.66V\).
• KCL Verification: \(I_T = I_1 + I_2\). For instance, \(0.6A = 0.38A + 0.22A\).

6. DISCUSSIONS

The above experiment was performed to verify Ohms law and Kirchhoff’s laws. In this experiment, we learned to handle an ammeter, voltmeter, and multimeter. We calculated the value of resistance using Ohms law, i.e., \(V=IR\). The obtained value of resistance is 25.81 Ω, whereas its standard value is 20 Ω.

Here we obtained a 29.05% error in measuring resistance. The error may be due to the least count of the ammeter and voltmeter. Similarly, the connection may have been loose, or the rheostat may have had high or low resistance.

7. CONCLUSION

Hence, Ohms Law and Kirchhoff’s Law have been verified.

8. PRECAUTIONS

• The readings should be taken very carefully.
• The rheostat should have a constant resistance.
• The least count should be included in the calculation.
• The electric circuit should be properly connected.