Parallel Resistor Equation
The following formulas are used to find total resistance in a parallel circuit. Let V be the applied voltage on the parallel circuit with resistors R1, R2 and R3 with total current ‘I’ flow through the circuit. As we know in the parallel circuit the current is different for all the components so, the current flowing through R1, R2 and R3 is I1, I2 and I3 respectively.
According to Ohm’s Law,
I = V / R
We know that the current I is divided among resistors R1, R2 and R3 as I1, I2 and I3 and voltage V is same. Therefore,
I = V/R
I1 = V/R1
I2 = V/R2
I3 = V/ R3
and
I = I1 + I2 + I3
Putting the values of I, I1, I2 and I3
V/R = V/R1 + V/R2 + V/R3
V/R = V × [1/R1 + 1/R2 + 1/R3]
1/R = [1/R1 + 1/R2 + 1/R3]
1/R = [1/R1 + 1/R2 + 1/R3]
or
R = (R1 × R2 × R3) / (R1 + R2 + R3)
where,
R1 is resistance of resistor R1
R2 is resistance of resistor R2
R3 is resistance of resistor R3
So, the total resistance in a parallel circuit is equal to the product of all the resistances connected in parallel divided by the sum of all the resistances in parallel.
Generalized Formula to Calculate Total Resistance in Parallel Circuit
Let R1, R2, …., Rn resistors are connected in parallel circuit. So, the total resistance of this circuit can be calculated by:
1/R = [1/R1 + 1/R2 + … + 1/Rn]
Total Resistance in a Parallel Circuit
The total resistance in a parallel circuit is obtained by taking the reciprocal of the sum of the reciprocals of the resistances of all the resistors connected in parallel. A parallel circuit is one of the important electric circuits. In a parallel circuit, the voltage is similar for all the components connected in parallel but the current flowing through the components is different.
In this article we will discuss the total resistance in a parallel circuit, the total resistance in parallel circuit formulas, and the advantages, disadvantages, and applications of parallel circuits. We will also solve some examples related to the total resistance in parallel circuits. Let’s start learning on the topic “Total Resistance in a Parallel Circuit”.
Table of Content
- Resistance
- Parallel Circuit
- Total Resistance in a Parallel Circuit
- Formulas
- Solved Examples
- Advantages and Disadvantages
- Applications