Electricity & Circuits Calculator

An electric circuit is a closed path along which charges move, driven by an electromotive force (a battery, a generator, a solar cell). Three rules govern almost every direct-current circuit: Ohm's law relates voltage, current, and resistance in each element (V = IR); Kirchhoff's current law (KCL) says the algebraic sum of currents into any node equals zero — charge is conserved; and Kirchhoff's voltage law (KVL) says the algebraic sum of voltages around any closed loop equals zero — energy is conserved. Series and parallel combinations are the two structures that, with these rules, solve any resistive circuit. Power dissipated in a resistor appears as heat (Joule heating) and obeys P = V·I = I²R = V²/R, three forms of the same number — pick whichever involves the quantities you already know.

Three quantities and one equation. Give the panel any two and it returns the third plus the power. The default sample (I = 2 A, R = 50 Ω) yields V = 100 V and P = 200 W — a small 100 W soldering iron running at full draw. The relation is linear for an ohmic conductor: metals at constant temperature, carbon-film resistors, and a few others follow V = IR with R roughly constant. Semiconductors, incandescent filaments, and thermistors do not — their resistance depends on voltage, current, or temperature, and the equation still works point by point but R is no longer a single number. The companion relation P = V·I is universal and always holds for DC circuits.

Components in series share one path; the same current flows through all of them, and the resistances add directly: R_eq = ΣR_i. The default sample (100 + 220 + 330 + 470 Ω) sums to 1,120 Ω; with a 12 V source the loop carries I = 12/1120 ≈ 10.71 mA and the four drops land at 1.07 V, 2.36 V, 3.54 V, 5.04 V — the familiar voltage divider rule, V_i = I · R_i. Series wiring is fragile in one sense: open any one resistor and the loop is broken, every device goes dark. The classic strings of Christmas-tree lights were the textbook example before switched to shunt-wired designs that keep the rest lit when one bulb fails.

Components in parallel all see the same voltage; their conductances (reciprocal resistances) add: 1/R_eq = Σ(1/R_i). The default sample (100, 200, 300 Ω) gives R_eq ≈ 54.55 Ω, with 12 V applied the total current is Itotal ≈ 0.22 A and the branches draw 120 mA, 60 mA, 40 mA respectively — the smallest resistor always takes the largest share, in inverse ratio. Two practical notes: a parallel combination is always less than the smallest individual resistor, which is the intuition for why connecting batteries in parallel adds capacity, not voltage. And in house wiring, every outlet is in parallel with every other, so a tripped breaker in one room does not extinguish the rest of the building.

A capacitor separates charge, accumulates it on two plates, and stores energy in the electric field between them. The book-keeping is Q = C·V for charge and E = ½C·V² for energy. The default sample (100 μF at 12 V) gives Q = 1,200 μC and E = 7.2 mJ. Doubling the voltage quadruples the energy; doubling the capacitance only doubles it — voltage is the lever, which is why camera flashes, defibrillators, and railguns charge to high voltage rather than simply using a bigger capacitor. In DC steady state no current flows through a capacitor (it is an open circuit); in AC the same element passes current proportional to frequency, and that is the basis of every filter, coupling, and timing circuit. Charging follows V(t) = V₀(1 − e^−t/RC): the RC time constant sets the pace, and after 5τ the capacitor is effectively full.

Two point charges feel a force along the line between them with magnitude F = k·|q₁q₂|/(ε_r·r²), attractive for opposite signs and repulsive for same signs; the Coulomb constant k = 8.988×10⁹ N·m²/C² is fixed by the geometry of empty space. The default sample (q₁ = +5 μC, q₂ = −3 μC, r = 0.1 m, vacuum) gives F ≈ 13.48 N, attractive — a modest weight-bearing pull from tiny charges because micro-coulombs are large charges in SI terms. The dielectric constant ε_r (80 for water, 3.5 for paper, 7 for glass) divides the force, which is why the same charges get weaker pulls inside matter; the molecular dipoles polarize and screen the field.

The three forms are algebraically identical, and choosing the right one saves you from the wrong one. P = V·I when both V and I are known; P = I²R when current and resistance are known — this is the form that explains why thin wires overheat in a short circuit; P = V²/R when voltage and resistance are known — the form that explains why a 120 V toaster draws 10 A from a 14 Ω nichrome element. The default sample (V = 12 V, I = 2 A) returns P = 24 W. A 60 W incandescent bulb on 120 V draws 0.5 A through a 240 Ω filament; the same 60 W on 12 V (a car bulb) draws 5 A through 2.4 Ω — voltage choice is current choice is wire-thickness choice.

• Voltage gets "used up" across a resistor. Voltage is the energy per coulomb delivered by the source; the same total is dissipated across all resistors in a loop. Saying "12 V dropped across the resistor" really means "the source delivered 12 V worth of energy to each coulomb passing through that resistor".
• Parallel resistors make a bigger total resistance. The opposite: parallel always decreases the equivalent resistance because every added branch is another path the current can take. R_eq < min(R_i) is the rule.
• Current is consumed by the load. Current is the same everywhere in a series loop and sums at every parallel node; charge is conserved (KCL). A 2 A current entering a fan is also 2 A leaving it.
• A capacitor "holds current". It holds charge. Once full, DC current stops. The energy is stored in the field, not in the carriers.

Related tools: Mechanics for the underlying force concepts, Formula Reference for the algebra, and Constants for ε₀ and the Coulomb constant.