Question

When a resistor is wired in a single loop with a battery, the current through the resistor is .What is the current through the circuit if you wire three more identical resistors in parallel with the first one?

Answer 1

Complete Question:

When a resistor is wired in a single loop with a battery, the current through the resistor is I .What is the current through the circuit if you wire three more identical resistors in parallel with the first one?

Answer:

Ip = 4*I

Explanation:

When several resistors are connected in parallel with a battery, the current through any resistor, can be found applying Ohm's Law:

$I =\frac{V}{R} (1)$

At the same time, applying KCL, we find that the total current is just the sum of the currents flowing through all resistors.

I = I₁ + I₂ + ...... + Iₙ

Replacing the value of each Iₙ by V/Rₙ, we get:

$I = \frac{V}{R1} + \frac{V}{R2} + ........... +\frac{V}{Rn} (2)$

From (1) and (2) we can get the value of the equivalent resistance Req, as follows:

$\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + ........... +\frac{1}{Rn}$

When R₁ = R₂ = R₃ = R₄ = R

Req = R/4

Replacing in the expression for I in (1) , we have:

$Ip =\frac{V}{\frac{R}{4}} = 4*\frac{V}{R} = 4*I$

⇒ Ip = 4*I