Resistors

Total resistance of resistors in series, parallel and combination circuits, with the current and voltage of each resistor.

What to find:

resistors in series

resistors in parallel

combination circuit (by a scheme)

Resistances are in ohms (1 kΩ = 1000 Ω). Write a combination circuit as an expression: “4 + (6 || 3)” is a 4 Ω resistor in series with 6 Ω and 3 Ω in parallel. || binds tighter than +.

Test yourself

The resistor calculator finds the total resistance of resistors in series, in parallel and in combination circuits, and — if the voltage is known — the current and voltage of each resistor.

Series

R = R₁ + R₂ + … + R_n

The current is the same in every resistor; the voltage divides in proportion to the resistances: V_i = I · R_i.

Parallel

¹/_R = ¹/_R₁ + ¹/_R₂ + … ; for two resistors R = ^R₁R₂/_{R₁ + R₂}

The voltage across every branch is the same and the currents add up. The total resistance is less than the smallest one.

Combination circuits

Write the circuit as an expression: “+” is series, “||” is parallel. For example “4 + (6 || 3)” is a 4 Ω resistor in series with 6 Ω and 3 Ω in parallel: 6 ‖ 3 = 2 Ω, total R = 4 + 2 = 6 Ω.