Series and Parallel Circuits

This laboratory examines direct-current resistor networks through two series circuits and two parallel circuits. The objective is to apply Ohm’s law, equivalent-resistance rules, Kirchhoff’s laws, and power equations, then compare theoretical calculations with values obtained in the PhET Circuit Construction Kit. The four original circuit cases are preserved because they demonstrate the core contrast clearly: current remains common in series, voltage remains common in parallel, and total power can be used as an independent consistency check (OpenStax, 2020).

An ideal simulation is especially useful for this purpose because component values can be set exactly and wires, sources, and meters can be treated as ideal. A physical laboratory would introduce resistor tolerance, internal source resistance, wire resistance, meter loading, contact resistance, and heating. Agreement between calculation and simulation therefore verifies the circuit model; it should not be interpreted as evidence that real measurements are always exact.

Governing Equations

Ohm’s law relates voltage, current, and resistance:

V = IR

where V is voltage in volts, I is current in amperes, and R is resistance in ohms. The same relationship may be written as I = V/R or R = V/I. For an ideal resistor, increasing applied voltage increases current, while increasing resistance reduces current for a fixed voltage.

Electrical power is the rate at which electrical energy is transferred:

P = VI

Combining this expression with Ohm’s law gives:

P = I²R and P = V²/R.

In a series circuit, components share one current path. The same current passes through every resistor, and equivalent resistance is the direct sum of the individual values:

R_eq = R₁ + R₂ + R₃ + …

Kirchhoff’s voltage law requires the total of all voltage drops around a closed loop to equal the source voltage. In a parallel network, every branch connects across the same two nodes and therefore experiences the same voltage. Equivalent resistance is calculated from:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + …

Kirchhoff’s current law requires current entering a junction to equal current leaving it. These relationships are described in the OpenStax treatments of Series circuits and Parallel circuits.

The simulation procedure is straightforward. Each network is calculated theoretically, then recreated in the Circuit Construction Kit: DC. An ammeter is inserted in series with the path or branch being measured, while a voltmeter is connected across the component. This distinction matters because placing an ideal ammeter directly across a source approximates a short circuit, while placing a voltmeter in series would prevent meaningful current flow in an ideal model.

Series Results

The first series circuit contains 20-ohm, 10-ohm, and 20-ohm resistors connected to a 10-volt source. Equivalent resistance is:

R_eq = 20 Ω + 10 Ω + 20 Ω = 50 Ω

Total current is therefore:

I = 10 V / 50 Ω = 0.20 A

Because the resistors are in series, the same 0.20 A passes through all three. The two 20-ohm resistors each drop 4 V, while the 10-ohm resistor drops 2 V. The drops sum to the source voltage:

4 V + 2 V + 4 V = 10 V

Power provides an additional check. Source power is 10 V × 0.20 A = 2.0 W. The resistor powers sum to the same value: 0.8 + 0.4 + 0.8 = 2.0 W. The simulation should therefore show the same current everywhere in the loop, voltage drops proportional to resistance, and total dissipated power equal to source power.

The second series circuit contains 20-ohm, 48-ohm, and 72-ohm resistors connected to a 70-volt source. Equivalent resistance is:

R_eq = 20 Ω + 48 Ω + 72 Ω = 140 Ω

Total current is:

I = 70 V / 140 Ω = 0.50 A

The common 0.50 A current produces voltage drops of 10 V, 24 V, and 36 V. Again, the drops add to the source voltage:

10 V + 24 V + 36 V = 70 V

The second case makes the voltage-divider principle especially clear. Because current is identical through every resistor, the largest resistance produces the largest voltage drop. The 72-ohm resistor accounts for 36 V of the 70 V source, while the 20-ohm resistor accounts for only 10 V. Source power is 70 V × 0.50 A = 35 W, equal to the sum of the three resistor powers.

Parallel Results

The first parallel circuit contains 3-ohm, 1.5-ohm, and 1-ohm resistors connected across a 6-volt source. The reciprocal-resistance calculation is:

1/R_eq = 1/3 + 1/1.5 + 1/1 = 2

Therefore:

R_eq = 0.50 Ω

Each branch is connected directly across the source and therefore has 6 V across it. The branch currents are 2 A, 4 A, and 6 A. Their sum is 12 A, which agrees with the equivalent-circuit calculation:

I_total = 6 V / 0.50 Ω = 12 A

This network demonstrates two quick checks for parallel circuits. First, equivalent resistance must be lower than the smallest branch resistance. Here, 0.50 Ω is lower than 1 Ω. Second, the lowest-resistance branch carries the greatest current. The 1-ohm branch carries 6 A, while the 3-ohm branch carries 2 A.

The second parallel circuit contains 15-ohm, 20-ohm, and 10-ohm resistors across a 90-volt source. The equivalent resistance is:

1/R_eq = 1/15 + 1/20 + 1/10 = 13/60

so:

R_eq = 60/13 Ω ≈ 4.62 Ω

Every branch receives 90 V. The branch currents are 6 A, 4.5 A, and 9 A, producing a total current of 19.5 A.

Again, the 10-ohm branch carries the greatest current and dissipates the greatest power. Kirchhoff’s current law is satisfied because 6 + 4.5 + 9 = 19.5 A. The source power of 90 V × 19.5 A = 1,755 W equals the total of the three branch powers.

Laboratory Interpretation

The four cases show the defining contrast between series and parallel networks. In series, adding resistance increases total resistance and reduces source current for a fixed supply. If the single path is opened anywhere, current stops throughout the network. In parallel, adding another branch reduces equivalent resistance and increases the total current demanded from an ideal source. One branch can be disconnected while the remaining branches continue operating.

These properties explain many practical circuit choices. Household lighting and outlets are connected primarily in parallel so that each load receives the supply voltage and can operate independently. Series arrangements are useful where the same current must pass through components or where intentional voltage division is required. Many practical circuits combine both structures.

The power calculations also illustrate why simulation can be safer than physical construction. The fourth circuit dissipates 1,755 W. Ordinary classroom resistors cannot safely handle hundreds of watts, and a 90-volt source is not a trivial laboratory supply. A physical implementation would require appropriately rated resistors, wiring, source protection, measurement equipment, and qualified supervision. The ideal PhET model allows the equations to be explored without delivering that real power.

Real measurements would also differ slightly from theoretical values. Commercial resistors have manufacturing tolerance; batteries and power supplies have internal resistance; meters influence the circuit; wires and contacts add resistance; and heating can change resistance while current flows. These differences should be interpreted as measurement and component effects rather than automatically treated as calculation errors.

A further practical distinction is fault behavior. In a series circuit, one open component interrupts the only current path, so the entire network stops conducting. In a parallel circuit, an open branch normally affects only that branch while the others continue to operate. A short circuit creates the opposite problem: an unintended very-low-resistance path can produce excessive current and dangerous heating. These fault patterns explain why fuses, circuit breakers, current limits, and correct component ratings are essential in real electrical systems even when the underlying equations are simple.

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The laboratory therefore confirms the major laws governing simple resistor networks. Ohm’s law predicts component current and voltage, Kirchhoff’s voltage law accounts for the voltage drops in series circuits, Kirchhoff’s current law accounts for branch currents in parallel circuits, and power conservation provides a final independent check. The numerical agreement across all four networks shows that the theoretical model and simulated circuit are internally consistent.

References

OpenStax. (2020). Series circuits. In Physics.

OpenStax. (2020). Parallel circuits. In Physics.

PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Circuit Construction Kit: DC.

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