# Combination of Resistors with Examples

**Combination of Resistors**

Resistors can be combined in two ways; series and parallel. Combination of more than one resistor is called equivalent resistor. We first look at the resistors in series;

**Resistors in Series**

a. In this types of circuit, amount of currents passing through the resistors are equal and this current comes from the battery.

**i=i _{1}=i_{2}=i_{3}**

b. Sum of the potential differences of each resistor is equal to total potential difference of the circuit or potential difference between the ends of battery.

**V=V _{1}+V_{2}+V_{3}**

c. If ,

**V _{1}=i_{1}.R_{1}**

** V _{2}=i_{2}.R_{2} **

**V _{3}=i_{3}.R_{3}**

**V=V _{1}+V_{2}+V_{3}**

**i.Req=i1.R1=i _{2}.R_{2}=i_{3}.R_{3}**

Since the currents are equal to each other;** **

**Req=R _{1}+R_{2}+R_{3}**

When you add new resistors to the circuit in series, equivalent resistance of the circuit increases.

**Resistors in Parallel**

a. Sum of the currents in each branch is equal to the current coming from battery.

**i _{t}=i_{1}+i_{2}+i_{3}**

b. Since the two ends of each resistor are connected to the same points, potential differences of each resistor are equal.

** V=V _{1}=V_{2}=V_{3}**

c.

When you add new resistors to the circuit in parallel, equivalent resistance of the circuit decreases.

d. If n number of resistors are combined in parallel like in the picture given below, we find the equivalent resistance of the circuit as;

Example: Find the, equivalent resistance, currents passing through each resistor and potential difference between the ends of each resistor of the circuit given below.** **

Since 3Ω and 6Ω resistors are in parallel, their equivalence becomes;

Since 4Ω and R_{eq1} resistors are in series, their equivalence becomes;

Since the equivalent resistance of 3Ω and 6Ω is 2Ω, potential difference between the ends of this resistor is;

**V=4A.2Ω=8volt**

Currents in the resistors are;

**i**_{3}**=8volt/3****Ω=8/3Amper**

**i _{6}=8volt/6**

**Ω=4/3Amper**

**i _{4}=4Amper
**

Potential difference between the ends of the 4Ω resistance is;

**V=i.R**

**V=4A.4****Ω=16volt**

**Electric Current Exams and Solutions**

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