Two resistors R1 and R2 are connected in series. Their values are 50 +...
Calculation of Equivalent Resistance in a Series Circuit
Introduction
In a series circuit, resistors are connected end-to-end, and electric current flows through each resistor in sequence. The total resistance of a series circuit is equal to the sum of the individual resistances.
Given Data
- Resistor 1 (R1) = 50 ± 0.5 Ω
- Resistor 2 (R2) = 20 ± 0.7 Ω
Calculating the Equivalent Resistance
The formula for calculating the equivalent resistance of a series circuit is:
R = R1 + R2 + R3 + ...
where R is the equivalent resistance and R1, R2, R3, etc. are the individual resistances in the circuit.
Using the given data, we can calculate the equivalent resistance as follows:
R = R1 + R2
R = (50 ± 0.5) Ω + (20 ± 0.7) Ω
R = 70 ± 1.2 Ω
Therefore, the equivalent resistance of the series circuit is 70 ± 1.2 Ω.
Explanation
In a series circuit, the resistors are connected end-to-end, so the same current flows through each resistor. As a result, the voltage is divided between the resistors in proportion to their resistance. The total resistance of the circuit is the sum of the individual resistances, so the equivalent resistance can be calculated by adding the resistances of each resistor in the circuit.
In this case, the resistances of R1 and R2 are given with uncertainties, which means that the equivalent resistance must also be calculated with an uncertainty. The uncertainties in the resistances are added in quadrature to find the uncertainty in the equivalent resistance.
Conclusion
The equivalent resistance of a series circuit can be calculated by adding the resistances of each resistor in the circuit. In this case, the equivalent resistance of a circuit with R1 = 50 ± 0.5 Ω and R2 = 20 ± 0.7 Ω was found to be 70 ± 1.2 Ω.