|Aim||Determination of the equivalent resistance of two resistors when connected in series and parallel.|
|Apparatus Required||Two resistors with known resistance values|
|Theory||When resistors are connected from a single point and rejoin the circuit, it is known as a parallel connection. The figure below shows three resistors, which provide three different routes for current to flow through the circuit. In a parallel circuit, the potential difference across each resistor is the same, but the current flowing through each resistor is not the same. The current splits as it travels through the circuit, and the total current flowing through the circuit can be calculated by adding the values of the current flowing through each resistor. Household electric distribution systems often use parallel circuits because they allow for the monitoring of current loss and prevention of short circuits. Different devices require different voltages to function, and if they are connected in series, the huge amount of current required by one device may damage the other devices. Parallel circuits are preferred to overcome such a situation. When resistors are connected in parallel with a combination of cells or batteries, the total current (I) is equal to the sum of the separate values of the current through each branch of the combination, i.e., I = I1 + I2 + I3 + …|
|Procedure||1 .Set up the breadboard by connecting it to the power supply.|
2 .Connect the two resistors in series on the breadboard.
3 .Measure the voltage across the two resistors using the digital multimeter.
4 .Measure the current flowing through the resistors using the digital multimeter.
5 .Calculate the equivalent resistance of the two resistors using Ohm’s law: R_eq = V / I, where V is the voltage across the resistors and I is the current flowing through the resistors.
6 .Disconnect the resistors from the breadboard and reconnect them in parallel.
7 .Measure the voltage across the resistors and the current flowing through them.
8 .Calculate the equivalent resistance of the two resistors when connected in parallel using Ohm’s law: R_eq = V / I, where V is the
9 .voltage across the resistors and I is the current flowing through the resistors.
|Results||The equivalent resistance of two resistors when connected in series was found to be 11.0 Ω and when connected in parallel was found to be 2.75 Ω. This experiment confirms that the equivalent resistance of resistors in series is the sum of their individual resistances, while the equivalent resistance of resistors in parallel is given by the reciprocal of the sum of the reciprocals of their individual resistances.|