# Resistors in series

If the resistors are connected as shown in the figure, the resistors are arranged in series. Resistor or electrical resistance in question can be in the form of resistor components, lights, or other electrical resistance.

The electric charge moves through resistance 1 (R_{1}) = the electric charge moves through resistance 2 (R_{2}) = the electric charge moves through resistance 3 (R_{3}). Electric current (I) is an electric charge that flows during a certain time interval (I = Q / t), hence the electric current through resistance 1 (I_{1}) = electric current through resistance 2 (I_{2}) = electric current through resistance 3 (I_{3}). Mathematically, the total electric current (I) = I_{1 }= I_{2} = I_{3}.

Conversely, the electric voltage (V) decreases when the electric charge moves through each resistor. Electricity voltage also called an electric potential difference, is an electric potential energy per unit of electric charge. Electricity voltage is reduced because electricity is used in each electrical resistance. So the total electrical voltage (V) is equal to the amount of electricity in each resistor. Mathematically, the total electric voltage (V) = V_{1 }+ V_{2 }+ V_{3}. V = I R so the equation of the electric voltage is V = I R_{1} + I R_{2} + I R_{3}. The electric current flowing on each resistor is equal so that this equation changes to V = I (R_{1} + R_{2 }+ R_{3}).

Based on the above equation it can be concluded that the total electrical resistance (R) or the equivalent resistance of the electrical resistance which is connected in series is equal to the sum of each electrical resistance, mathematically R = R_{1} + R_{2} + R_{3}. If there are only two resistors in series, the equivalent resistor (R) = R_{1 }+ R_{2}. If there are four resistors in series, the equivalent resistor (R) = R_{1} + R_{2 }+ R_{3} + R_{4}. Likewise, if there are five or more five resistors that are connected in series.

Sample problem 1:

If known R_{1 }= 2 Ω, R_{2} = 3 Ω and R_{3} = 4 Ω. All three resistors are connected in series. What is the value of the equivalent resistor? (Ω = Ohm).

Solution:

R = R_{1 }+ R_{2} + R_{3} = 2 + 3 + 4 = 9 Ω.

This result shows that the equivalent resistance is greater than the value of the resistors connected in series.

Sample problem 2:

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

(a) The equivalent resistance

(b) Electric current through each resistor

Solution:

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

(b) I = V / R = 12 Volt / 100 Ω = 0.12 A