Resistors in parallel:

If the same voltage is applied across each resistor, then they are said to be connected in parallel. In a parallel circuit, the total current flowing out of the source is equal to the sum of the individual currents flowing through each branch (resistor). The resistors are connected in parallel, i.e., the first of each resistor connected to a common point and second end of each resistors are connected to a common point as shown in Fig.

Imagine as previous modules assume a water pipe as a conductor,, water as a current, a water tank as a powerhouse, and water pressure as voltage. In a parallel connection, assume three water taps are connected to the outlet pipe of the tank in parallel, just like in a in a circuit, but in place of resistors, when these three taps are open, then automatically the water drains fast because the taps are connected in parallel, same as in a circuit, but the water pressure is the same, just like voltage.

Consider three resistors R₁ , R₂ , R₃ are connected in parallel across a battery as shown in figure below then the total resistance R_T is given by

According to Ohm’s Law

Here the voltage is dividing across each resistor, then

Voltage drop across each resistance R₁, I₁ = V/ R₁

Voltage drop across each resistance R₂, I₂ = V/R₂

Voltage drop across each resistance R₃, I₃ = V/ R₃

The total current is entered in to circuit is equal to the sum individual current through each resistors

I = I₁ + I₂+I₃

= V/ R₁+ V/R₂+ V/ R₃

=V(1/R₁+1/R₂ +1/ R₃)

I/V= 1/R₁+1/R₂ +1/ R₃

or

1/v/I =1/R₁+1/R₂ +1/ R₃

or

1/R_T = 1/R₁+1/R₂ +1/ R₃

Characteristics of parallel circuit:

(i) 1. There is the same potential difference across all resistances in parallel

(ii) 2. The total current is equal to the sum of all individual currents.

(iii) The reciprocal of equivalent or total resistance is equal to the sum of the reciprocal of all individual resistances connected in parallel.

(iv) 3. Different resistances exhibit different values of currents.

Key Points:

(i) • The equivalent resistance is less than the smallest of all the resistances connected in parallel.

(ii) If ‘n’ resistors, each of having same resistance (R ohms) are connected in parallel then, R_eq=R/n

Application of Parallel circuits:

Parallel circuits are common in use. All the home appliances are connected in parallel due to their characteristics. An individual control over all parallel connected devices can be archived so that if one of the devices is damaged, no device can be interrupted in a parallel connection.