Question

Deduce the expression for the equivalent resistance of the parallel combination of three resistors R₁, R₂ and R₃ Consider the following electric circuit:

(a) Which two resistors are connected in series? 

(b) Which two resistors are connected in parallel? 

(c) If every resistor of the circuit is of 2 Ω, what current will flow in the circuit?

Comments

This answer is helping so much to answer any questions in exam

Answer 1

Consider the following parallel circuit shown below: Let I₁, I₂ and I₃ be the current flow through the resistor R₁, R₂ and R₃ connected in parallel. Using Ohm’s law, current through each resistor is

I₁ = V/R₁, I₂ = V/R₂ and I₃ = V/R₃

Let their equivalent resistance be R_p then

V = I R_p ⇒ I = V/R_p

Total current through the circuit is

(a) R₅ and R₄ with Parallel combination of R₂ and R₃ are in series 

(b) R₂ and R₃ are in parallel. 

(c) R₂ and R₃ in parallel gives R_p = 1 Ω R_p, R₅ and R₄ are in series. 

So, R_eq = 5 Ω R₁ is not to be taken as it is shorted.

Current flowing, l = V/R = 5/5 = 1A

Comments

What does the word shorted mean here , in the second last line

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A short circuit is simply a low resistance connection between the two conductors supplying electrical power to any circuit. This results in excessive current flow in the power source through the 'short,' and may even cause the power source to be destroyed.