Resistors are in parallel when their two terminals connect to the same nodes.
Resistors are often connected in series or in parallel for creating more complex networks. The voltage across resistors in parallel will be the same for each resistor. But, the current will be in proportion to the resistance of each individual resistor.
The purpose of finding the equivalence resistance is that we can replace any number of resistors connected in a parallel combination by the equivalent resistance of the parallel combination resistors.
If two or more resistors are connected in parallel, then the potential difference across all the resistors is the same. Resistors in parallel connection are connected to the same nodes from both ends.
This can be identified by the presence of more than one way for the current to flow. The potential difference across the resistors is the same as that across the resistor which is equal to the supply potential.
Resistors in Parallel:
case 1.
Consider the following circuit where four resistors R1, R2, R3 and R4 are connected in parallel:
Case2:
Consider the following circuit where four resistors R1, R2 and R3 are connected in parallel:
case3.
Consider the following circuit where four resistors R1 and R2 are connected in parallel:
Case4.
Consider the following circuit where four resistor R1
The total current in the circuit can be calculated by two methods.
First method is to calculate individual currents flowing through each resistor.
The supply voltage is V,
If I1 is the current flowing through the resistor R1, then according to Ohm’s law
I1 = V / R1
Similarly if I2 is the current flowing through the resistor R2, then according to Ohm’s law
I2 = V / R2
If I3 is the current flowing through the resistor R3, then according to Ohm’s law
I3 = V / R3
And if I4 is the current flowing through the resistor R4, then according to Ohm’s law
I4 = V / R4
If I (t) is the total current in the circuit, then according to Kirchhoff’s Current law,
I(t) = I1 + I2 + I3 + I4
The equivalent resistance R(t) of the circuit is
1/R(t) = (1/ R1) + (1/R2) + (1/ R3) + (1/R4)
This single resistor can be used to replace all the resistors in the parallel combination.
∴ I(t) = V/R(t)
Creating android application for parallel resistance calculation.
Screen1: Case 1
Screen1: Case 2
Screen1: Case 3
Screen1: Case 3
Main Page:
The below blocks for in which parallel circuit is taken for calculation. i.e. case 1, Case2, Case3, Case4 using the check box.
Initialize the input varailble and math block for calculation as mention above.
Applications
The concept of resistors in parallel is used in the analysis of Wheatstone bridge circuit. Resistors in parallel combination act as Current Divider Circuit. This current divider concept is use full in applications like Analog to Digital Converters and Digital to Analog Converters.