Resistors in Parallel

 Parallel Configuration

In a parallel configuration:

• Each resistor has its terminals connected across the same two points in the circuit.
• The voltage across each resistor is the same.
• The current divides among the individual resistors.
• 

In a parallel circuit, the reciprocal of the total resistance (1/ Rp) is equal to the sum of the reciprocals of the individual resistances. This configuration leads to a decrease in the overall resistance
compared to the individual resistances due to multiple paths for current flow.

Total Current (I) = V / Rp${\mathrm{<br>}}_{}$

The parallel combination of components in an electrical circuit offers several advantages:

• Electrical devices designed to work for different current rating and same voltage works in parallel combination. Components in parallel share the same voltage across their terminals.
• Parallel circuits provide redundancy. If one component fails, others continue to operate, ensuring the circuit's functionality.
• Components can be added or removed without affecting the operation of other elements, making troubleshooting and upgrades more straightforward.

Note:

For two Resistors R1 and R2 , the equivalent Resistance is 1/Rp${\mathrm{<br>}}_{}$ = 1/R1 + 1/R2

or Simply Rp${\mathrm{<br>}}_{}$ = R1 x R2 / (R1 + R2)

When all resistors in parallel combination has same resistance i.e. R1 = R2 = … = Rn = R

Rp = R / n where n is the number of resistors in parallel combination

Current in each branch i.e. I1 = I2 = … = I = Itotal${\mathrm{<br>}}_{}$ / n

Solved Numerical:

There are two resistors R1 and R2 having resistance equal to 20 Ω and 30 Ω respectively are connected in parallel in an electric circuit. If the potential difference across the electric circuit is 5 V, find the electric current flowing through the circuit and the total resistance of the resistors.

Given: R1 = 20 Ω, R2 = 30 Ω, Potential difference (V) = 5 V

To find Total resistance (R) =?

Electric current (I) through the circuit =?

We know that in parallel combination, the reciprocal of total resistance is;

1/R = 1 / R1 + 1 / R2

= 1 / 20 Ω + 1/ 30 Ω

R = 20 x 30 / (20+30)

R = 12 Ω

Now, electric current through the circuit I = V / R

Or, I = 5 V ÷ 12 Ω = 0.416 A

Thus, total resistance R = 12 Ω

Electric current (I) through the circuit = 0.416 A