Resistors in Parallel
In the figure given below, three resistors are shown which are connected in parallel with a battery of voltage V. In this type of connection, the resistors are usually connected on parallel wires originating from a common point. In this case, the voltage through each resistor is the same. The figure on the right side shows the equivalent resistance of the three resistances. The diagram given below shows the resistor added in parallel combination.
The derivation of equivalent resistance for resistors in parallel is discussed below:
The relation between voltage and current is given by,
V = IR
It can be rewritten as,
I = V/R
The voltages across individual resistors will be,
I1 = V/R1 , I2 = V/R2, I3 = V/R3
The total current across all the resistances will be,
I = I1 + I2 + I3
Substituting the expressions for individual voltages,
I = V/R1 + V/R2 + V/R3
Let the equivalent resistance be R,
V/R = V/R1 +V/R2 + V/R3
Upon Simplifying the above equation, the relation becomes,
In general for resistance R1, R2, R3,…
Equivalent Parallel Resistance
Thus the equivalent resistance in parallel combination is given below:
Resistors in Series and Parallel Combinations
Resistors are devices that obstruct the flow of electric current in the circuit. They provide the hindrance to the path of the current which flows in the circuit. Resistors consume the current in any circuit and convert them to other forms of energy as required. Various resistors can be added to the circuits as per our requirements. Two or more resistors can easily be added in particular sequences. The addition of resistors can be achieved using any of the two methods i.e. Series Combination and Parallel Combination. In this article, we will learn about the arrangement of Resistors in Series and Parallel combinations and others in detail.
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