Calculators/Physics/Ohm's Law and Equivalent Resistance

Ohm's Law and Equivalent Resistance

U · I · R · P · series and parallel resistance

Ohm's Law and Equivalent Resistance — illustration

Enter any two quantities — I will compute the third from I = U/R.

U
12
V
I
3
A
R
4
Ω
P
36
W

Ohm's law: U = I·R. Power: P = U·I = U²/R = I²·R.

Ohm's law relates voltage, current and resistance:

U=I⋅RP=U⋅I=U2R=I2RU=I\cdot R \qquad P=U\cdot I=\frac{U^2}{R}=I^2 R

Enter any two of the quantities UU, II, RR — the calculator finds the third and the power PP.

The second mode computes the equivalent resistance of a circuit. In a series connection the resistances add up, and in a parallel one their reciprocals add up:

Rs=∑Ri1Rr=∑1RiR_s=\sum R_i \qquad \frac{1}{R_r}=\sum\frac{1}{R_i}

The resistance of a parallel connection is always smaller than the smallest resistor.

Examples

U = 12 V, R = 4 Ω
→ I = 3 A, P = 36 W
Series: 10 Ω + 20 Ω + 30 Ω
→ R_z = 60 Ω
Parallel: 10 Ω and 20 Ω
→ R_z = 1/(1/10+1/20) ≈ 6.67 Ω

Frequently asked questions

Why is the parallel resistance smaller?+

Because the current has more paths to flow through — an extra branch lowers the total resistance. The resultant resistance of a parallel connection is always smaller than the smallest resistor.

How do you compute the power dissipated in a resistor?+

With three equivalent formulas: P = U·I = U²/R = I²·R. You pick the one that matches the data you have.

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