Why does adding a resistor in parallel decrease the total resistance, but adding one in series increases it?

In parallel, you create an additional path for current to flow. This is analogous to adding more lanes to a highway—it reduces the overall opposition to traffic. Mathematically, adding another term 1/R to the sum of reciprocals increases the total value of 1/R_total, meaning R_total itself must get smaller. In series, you are lengthening the single path, increasing the total opposition to flow.

In a parallel circuit, if one bulb burns out (opens), do the others get brighter or stay the same?

In a pure parallel circuit, each bulb has the full source voltage across it. If one bulb burns out and opens, that branch is removed. The total resistance of the circuit increases slightly (one less parallel path), so the total current from the battery decreases. However, the remaining bulbs still have the full voltage across them, so their current and brightness remain unchanged.

Does the simulator's model apply to real-world household wiring?

Yes, the core principles apply. Household outlets are wired in parallel so that each appliance receives the same standard voltage (e.g., 120V) and operates independently. The simulator's simplification of ideal wires is reasonable for understanding topology, but real wires have small resistance, and safety devices like fuses rely on the current-division principles shown here.

How do Kirchhoff's laws relate to what I see in the simulator?

Kirchhoff's Voltage Law (KVL) is demonstrated in the series loop: the sum of the voltage drops across the resistors equals the battery voltage. Kirchhoff's Current Law (KCL) is shown at the parallel junctions: the total current from the battery equals the sum of the currents entering each parallel branch. The simulator's numerical displays and visual current flow embody these conservation laws.

Series & Parallel

Understanding how resistors combine to control current flow is a cornerstone of circuit analysis. This simulator models the fundamental behavior of resistors connected in series and in parallel configurations, powered by a simple DC voltage source. It visually demonstrates Ohm's Law (V = IR) and Kirchhoff's circuit laws in action. For series circuits, the total resistance (R_total) is the sum of the individual resistances (R_total = R1 + R2 + ...). This results in a single, shared current throughout the loop, with voltage drops proportional to each resistor's value. In parallel, the reciprocal of the total resistance equals the sum of the reciprocals (1/R_total = 1/R1 + 1/R2 + ...), leading to a lower total resistance than the smallest individual resistor. Here, the full source voltage appears across each branch, but the current divides, with more current taking the path of least resistance according to I = V/R for each branch. The model simplifies real-world circuits by assuming ideal wires with zero resistance, perfect connections, and resistors that obey Ohm's Law perfectly across all conditions. By interacting with the simulator, students can directly observe how manipulating resistor values and circuit topology changes the total resistance, alters the current distribution, and affects the brightness of symbolic bulbs. This builds an intuitive grasp of equivalent resistance and the conservation of current and energy in multi-path circuits.

Who it's for: High school physics students and introductory undergraduate engineering students learning DC circuit fundamentals and network analysis.

Key terms

Ohm's Law
Series Circuit
Parallel Circuit
Equivalent Resistance
Kirchhoff's Current Law
Kirchhoff's Voltage Law
Current Division
Resistor Network

How it works

Compare equivalent resistance and currents for the same two resistors: in series they add (larger R, smaller current); in parallel the equivalent resistance is smaller than either branch, so the battery supplies more total current while each branch sees the full voltage V.

Key equations

R_s = R₁ + R₂, I_s = V / R_s

1/R_p = 1/R₁ + 1/R₂, I_tot = V/R_p, I₁ = V/R₁, I₂ = V/R₂

Frequently asked questions

Why does adding a resistor in parallel decrease the total resistance, but adding one in series increases it?: In parallel, you create an additional path for current to flow. This is analogous to adding more lanes to a highway—it reduces the overall opposition to traffic. Mathematically, adding another term 1/R to the sum of reciprocals increases the total value of 1/R_total, meaning R_total itself must get smaller. In series, you are lengthening the single path, increasing the total opposition to flow.
In a parallel circuit, if one bulb burns out (opens), do the others get brighter or stay the same?: In a pure parallel circuit, each bulb has the full source voltage across it. If one bulb burns out and opens, that branch is removed. The total resistance of the circuit increases slightly (one less parallel path), so the total current from the battery decreases. However, the remaining bulbs still have the full voltage across them, so their current and brightness remain unchanged.
Does the simulator's model apply to real-world household wiring?: Yes, the core principles apply. Household outlets are wired in parallel so that each appliance receives the same standard voltage (e.g., 120V) and operates independently. The simulator's simplification of ideal wires is reasonable for understanding topology, but real wires have small resistance, and safety devices like fuses rely on the current-division principles shown here.
How do Kirchhoff's laws relate to what I see in the simulator?: Kirchhoff's Voltage Law (KVL) is demonstrated in the series loop: the sum of the voltage drops across the resistors equals the battery voltage. Kirchhoff's Current Law (KCL) is shown at the parallel junctions: the total current from the battery equals the sum of the currents entering each parallel branch. The simulator's numerical displays and visual current flow embody these conservation laws.