Combination of resistors Practical

aSTUDY OF SERIES AND PARALLEL COMBINATION OF RESISTORS USING PHET SIMULATION Materials Required Phet Simulation – DC virtual LabApparatus/Components in the Simulation• Battery• Resistors• Wires• Switch• Ammeter• Voltmeter TheorySeries Combination of ResisitanceTwo or more resistances are said to be connected in series when they are connected end to end and the same current flows through each of them in turn. In this case, the equivalent or the total resistance equals the sum of the number of individual resistances present in the series combination. Mathematically, the equivalent resistance of any number of resistances (R1, R2, R3${\displaystyle R_1,R_2,R_3}$ Connected in series is given as:

Req = R1 + R2 + R 3 $$R_{eq}=R_1+R_2+R_3$$Parallel Combination of resistanceTwo or more resistances are said to be connected in parallel connected when they are connected between two points and each has a different current direction. The current is branched out and recombined as the branches intersect at a common point in such circuits. Mathematically, the equivalent resistance of any number of resistances ) connected in parallel is given as:

1

Req=1

R1+1

R2+1

R3$$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$$ProcedureFor series combination1. Open the PhET Circuit Construction Kit – DC Virtual Lab.2. Construct a circuit containing a battery, switch and two resistors connected in series.3. Use R₁ = 10 Ω, R₂ = 20 Ω and battery voltage V = 12 V.4. Close the switch. 5. Place the ammeter at different points in the circuit and record the current.6. Use the voltmeter to measure voltage across R₁, voltage across R₂, and total voltage across the combination.7. Calculate the theoretical equivalent resistance using Rs = R₁ + R₂.8. Calculate the theoretical current using I = V/Rs.9. Compare theoretical values with simulation values. For Parallel combination17. Construct a new circuit containing two resistors connected in parallel.18. Use R₁ = 10 Ω, R₂ = 20 Ω and battery voltage V = 12 V.19. Close the switch.20. Measure the total current supplied by the battery.21. Measure the current through R₁ and the current through R₂.22. Measure the voltage across each resistor.23. Calculate the theoretical equivalent resistance using 1/Rp = 1/R₁ + 1/R₂.24. Calculate the theoretical total current using I = V/Rp.25. Compare theoretical values with the simulation results.ObservationFor Series

Quantity	Observed Value
Resistance R₁	10 Ω
Resistance R₂	20 Ω
Battery voltage	12 V
Current before R₁	________ A
Current between R₁ and R₂	________ A
Current after R₂	________ A
Voltage across R₁	________ V
Voltage across R₂	________ V
Total voltag	_______ V
Equivalent resistance	________ Ω

For Parallel

Quantity	Observed Value
Resistance R₁	10 Ω
Resistance R₂	20 Ω
Battery voltage	12 V
Voltage across R₁	________ V
Voltage across R₂	________ V
Current through R₁	________ A
Current through R₂	________ A
Total current	________ A
Equivalent resistance R	________ Ω

CalculationSeries CombinationGiven: R₁ = 10 Ω, R₂ = 20 Ω, V = 12 Va. Equivalent resistance: Rs = R₁ + R₂ = __________b. Total current: I = V/Rs = __________c. Voltage across R₁: V₁ = IR₁ = __________d. Voltage across R₂: V₂ = IR₂ = __________ Parallel CombinationGiven: R₁ = 10 Ω, R₂ = 20 Ω, V = 12 Va. Equivalent resistance: 1/Rp = 1/10 + 1/20; Rp = __________b. Current through R₁: I₁ = V/R₁ = __________c. Current through R₂: I₂ = V/R₂ = __________d. Total current: I = I₁ + I₂ = __________ConclusionFor Series CombinationComplete the following statement based on your observations:When resistors are connected in series, the __________ remains the same through all the resistors, while the __________ is divided among the resistors. The equivalent resistance is equal to ______________________________.Therefore, the equivalent resistance of a series combination is ______ than the resistance of any individual resistor.For ParallelWhen resistors are connected in parallel, the ______ across each resistor remains the same, while the ______ divides among the different branches. The total current is equal to ______________________________.The equivalent resistance of a parallel combination is ______ than the resistance of the smallest individual resistor. Overall Conclusion Write your conclusion in your own words after completing the simulation.From the PhET simulation, I observed that in a series combination, ________________________________.The equivalent resistance of resistors in series is ________________________________.In a parallel combination, ________________________________.The equivalent resistance of resistors in parallel is ________________________________.Therefore, the simulation verifies that ________________________________.