Quick answer Ohm's law is V = I × R. The combined resistance in series is R = ΣRᵢ, and in parallel 1/R = Σ(1/Rᵢ). Power dissipation is P = V × I = I²·R.
Slide V, I, R sliders and watch current flow animate in real time. Switch to circuit mode to analyze series, parallel, and mixed resistor networks instantly.
How to read: electron (blue dot) speed & density are proportional to current I=V/R. Raise V → faster & denser; raise R → slower & sparser. The resistor's red glow is proportional to dissipated power P=I²R.
V–I characteristic (Ohm's law)
Element
R (Ω)
I (mA)
V (V)
P (mW)
Circuit diagram
CAE connection: In electrical conduction FEA (Ansys Maxwell, COMSOL), Ohm's Law is applied volumetrically as $\mathbf{J}= \sigma\mathbf{E}$. Kirchhoff's laws are formulated as the nodal admittance matrix, solved by the same sparse direct solvers used in structural FEA.
Theory & Key Formulas
$$V = I \times R$$
$$I = \frac{V}{R}, \quad R = \frac{V}{I}$$
$$P = VI = I^2 R = \frac{V^2}{R}$$
What is Ohm's Law & Circuit Analysis?
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What exactly is Ohm's Law? I see the equation V = I x R, but what does it really mean for a circuit?
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Basically, it's the fundamental relationship between voltage (V), current (I), and resistance (R) in a simple conductor. Think of it like water in a pipe: voltage is the water pressure, current is the flow rate, and resistance is how narrow the pipe is. In practice, if you increase the voltage (pressure), more current (flow) will push through a fixed resistance. Try moving the "Voltage V" slider in the simulator above—you'll see the current change instantly.
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Wait, really? So if I know any two of these, I can find the third. But what happens when I have more than one resistor, like in the "Series" or "Parallel" connection options?
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Great question! That's where circuit analysis comes in. For instance, in a series circuit, the current is the same everywhere, but the voltage is split between resistors. The total resistance just adds up. A common case is old-school Christmas lights. In the simulator, switch the connection type to "Series" and add more resistors. You'll see the total resistance increase, which for a fixed source voltage, makes the overall current drop.
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Okay, that makes sense for series. But parallel seems weird—why does adding a resistor in parallel decrease the total resistance? That seems backwards!
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It feels counterintuitive, but it's like adding an extra lane to a highway. More lanes (parallel paths) make it easier for traffic (current) to flow, so the overall resistance drops. For instance, homes are wired in parallel so you can turn on a light without affecting your TV. Try it in the simulator: set the connection to "Parallel" and increase the number of resistors. Watch the equivalent resistance value shrink, allowing more total current from the source.
Physical Model & Key Equations
The core governing principle for a single resistive element is Ohm's Law, which states that the voltage across a conductor is directly proportional to the current flowing through it.
$$V = I \times R$$
V is Voltage (Volts, V) – the electrical "push". I is Current (Amperes, A) – the flow of charge. R is Resistance (Ohms, Ω) – the opposition to current flow.
When multiple resistors are combined, the equivalent resistance depends on their configuration. The power dissipated as heat (Joule heating) is also a critical result.
In a series circuit, the same current flows through all components. In parallel, the same voltage is across each branch. The power equation shows how electrical energy is converted to heat, which is vital for thermal design.
Frequently Asked Questions
First, please check whether the circuit mode is set to 'Series,' 'Parallel,' or 'Mixed.' If none is selected, the animation will not work. Additionally, setting the resistance to 0Ω may cause the current to display as infinite and stop the animation. Please set the resistance to 1Ω or higher.
In a parallel connection, the number of current paths increases, making it easier for current to flow overall. According to Ohm's law (V=IR), for the same voltage, a lower resistance results in higher current, so the total resistance is smaller than any individual resistance. Example: The total resistance of a 2Ω and 3Ω parallel combination is 1.2Ω.
No, this tool is designed exclusively for DC circuits. AC circuits require concepts such as impedance and phase difference, which cannot be accurately calculated using Ohm's law alone. Please use a different simulator for AC calculations.
The current version does not have an automatic unit switching feature. However, you can manually set the slider values to 1/1000 to perform calculations in milli-units. For example, input 5V as 0.005V and 2A as 0.002A, then multiply the results by 1000 when reading them.
Ohm's Law and Electric Power
The current $I$ flowing through a conductor is proportional to the applied voltage $V$ and inversely proportional to the resistance $R$ (Ohm's law).
$V = I R, \qquad P = V I = I^2 R = \dfrac{V^2}{R}$
Here $V$ is the voltage [V], $I$ the current [A], and $R$ the resistance [Ω]. The power dissipated $P$ [W] can be written three ways, chosen according to which quantities can be measured. All power dissipated in a resistor becomes Joule heat.
In series the equivalent resistance increases; in parallel it decreases (becoming smaller than the smallest resistor). Household outlets are wired in parallel, so each appliance receives the same voltage. In this simulator you can explore the relationship among $V$, $I$, and $R$.
Real-World Applications
Electronics Design & PCB Layout: Engineers use these principles daily to design circuits. Calculating voltage drops across series resistors ensures microchips get the correct operating voltage. Simulating parallel paths helps size traces to handle current without overheating, which you can explore by changing resistance and watching the power value change in the tool.
Power Systems & Home Wiring: All household circuits are parallel to allow independent operation of appliances. The total current drawn from the mains must be calculated to prevent overloading and tripping circuit breakers, a direct application of parallel resistance and Ohm's Law.
Sensor & Measurement Systems: Many sensors, like temperature-dependent thermistors, work by changing resistance. A known voltage is applied, and the measured current (via Ohm's Law) reveals the sensor's reading. This is fundamental in data acquisition systems.
CAE & Electro-Thermal Simulation: In tools like ANSYS Maxwell or COMSOL, the $I^2R$ power loss from these equations becomes a volumetric heat source. This is crucial for simulating how much a motor winding will heat up or ensuring a power electronic device doesn't melt, linking circuit analysis directly to thermal and structural performance.
Common Misconceptions and Points to Note
When you start playing with this simulator, there are a few points you should be aware of. First, you might think "if you increase the voltage, the current will always increase proportionally," but that's only true if the resistance is constant. In practice, for example, applying too much voltage to an LED causes its internal resistance to drop sharply, allowing a large current to flow and instantly destroying it (a phenomenon called avalanche breakdown). Keep in mind the difference between experimenting in the simulator by changing V with a fixed "resistor R" and real-world components where the "resistor R" itself can change.
Next, calculation errors for equivalent resistance in parallel circuits. When you put two resistors in parallel, if their values are the same, the equivalent is simply half. However, if the values are vastly different, the result can be counter-intuitive. For example, with R1=10Ω and R2=1000Ω in parallel, the equivalent resistance is about 9.9Ω, pulled almost entirely by the smaller resistor value. It helps to think that "the path with less resistance (the easier path for current) dominates." Try setting extreme values in the simulator and verify the calculation results.
Finally, remember that the "power supply" in the simulator is an ideal voltage source. Real batteries and power supplies have internal resistance, so their terminal voltage drops when you draw a large current. The phenomenon where car headlights dim momentarily when starting the motor is an example. Since this tool is for foundational understanding, the next step is to consider models that include internal resistance.
Enter voltage in volts using vOhmNum input or drag vSlider to set supply voltage (typical range 1–24V for DC circuits)
Set resistance in ohms via rOhmNum input or rSlider; common values include 100Ω (LED), 10kΩ (sensor pull-up), 220Ω (current-limiting resistor)
Simulator calculates current (I = V ÷ R in mA), power consumption (P = V × I in watts), and energy per hour in watt-hours
Adjust vsSlider to model voltage source variations and observe real-time changes in all electrical parameters
Worked Example
Industrial 12V DC power supply driving a heating element with 48Ω resistance: V=12V, R=48Ω yields I = 12÷48 = 0.25A (250mA), P = 12×0.25 = 3W. Over one hour, energy consumption = 3Wh. For a sensor circuit at 5V with 10kΩ pull-up resistor: I = 5÷10000 = 0.5mA, P = 5×0.0005 = 2.5mW, demonstrating low-power logic-level operation.
Practical Notes
Temperature coefficient: Ohmic resistance increases ~0.4% per °C for copper conductors; recalculate for high-current DC applications (e.g., motor starters) experiencing thermal rise
Power dissipation sizing: Select resistor wattage rating exceeding calculated P by minimum 2× safety margin; 3W resistor dissipating 2.5W generates 60–80°C surface temperature
Voltage drop across internal source resistance: Real 12V supply with 0.5Ω internal resistance supplying 5A load shows only 11.75V at load terminals; account for this in precision circuits