# Resistors in parallel

If the resistors are connected as in the figure, the resistors are connected in parallel.

The electric current (electric current = electric charge that flows during a time interval) that enters the junction point is the same as the electric current exit from the junction point. There are several junctions so that the total electric current = the amount of electric current flowing in each junction. Mathematically I = I_{1 }+ I_{2} + I_{3}. While the electric potential difference or electrical voltage in each junction is the same.

I = V/R so the above equation changes to I = V/R_{1} + V/R_{2} + V/R_{3}. The electric voltage is equal so this equation changes to I = V (1/R_{1} + 1/R_{2} + 1/R_{3}). If the equivalent resistance is 1/R then I = V (1/R). Thus 1/R = 1/R_{1} + 1/R_{2} + 1/R_{3}.

Parallel circuits have the advantage, if the electric current to one of the resistors broken, the electric current continues to flow to the other resistors. Whereas in series, if an electric current in one resistor broken, then all resistors not be electrified.

Sample problem 1:

Known that R_{1 }= 2 Ω, R_{2} = 3 Ω. Both resistors are parallel. What is the value of the equivalent resistor? (Ω = Ohm).

Solution:

1/R = 1/R_{1 }+ 1/R_{2} = 1/2 + 1/3 = 3/6 + 2/6 = 5/6

R = 6/5 = 1.2 Ω.

This result shows that the equivalent resistor value is smaller than the value of each parallel resistor.

Sample problem 2:

Two R_{1} = 50 Ω and 50 resistor resistors are connected in series and parallel, connected to a 12 Volt battery. Determine:

(a) The equivalent resistance

(b) Electric current through each resistor

Solution:

(a) Resistors in series:

R = R_{1} + R_{2} = 50 Ω + 50 Ω = 100 Ω.

Resistors in parallel:

1/R = 1/R_{1} + 1/R_{2} = 1/50 + 1/50 Ω = 2/50

R = 50/2 = 25 Ω

(b) Resistors in series:

I = V / R = 12 Volt / 100 Ω = 0.12 A

Resistors in parallel:

I = V / R = 12 Volt / 25 Ω = 0.48 A

This result shows that the total electric current flowing in the parallel circuit is greater, while the total electric current flowing in the series is smaller.