Question

Find out the equivalent resistance between A & C​

Answer 1

Answer- The above question is from the chapter 'Electricity'.

Let's know about resistance.

Resistance- It is the property of a conductor, semi-conductor or insulator to resist the flow of charges.

R = V/I

where R = Potential difference between two end points and I = flow of current.

Resistance is generally measured in Ohms. (Ω)

R = $\frac{\rho * l}{A}$

where ρ = resistivity, l = length of wire and A = Area of cross-section of wire.

R ∝ l

R ∝ ρ

R ∝ 1/A

Resistors can be connected in basically 2 ways:

1. Series Combination

2. Parallel Combination

Concept used: 1) In series combination,

Effective Resistance = Sum of all resistances (R₁ + R₂ + _ _ _ + Rₙ)

where n = number of resistors connected.

2) In parallel combination,

Effective Resistance = $R_p$ which is given by

$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + ... + \dfrac{1}{R_n}$

where n = number of resistors connected.

Given question: Find the resistance between the points A & C.

(Figure has been attached in the question.)

Answer: Let's reconstruct the figure.

1. Current is flowing from A.

2. Now, it gets three paths to flow.

3. Net resistance can be found out between points A and C.

(See the diagram attached.)

Resistors 1 and 2 each of R Ω are connected in series.

$R_{s_{1}}$ = R + R = 2R Ω

Similarly, 4 and 5 each of R Ω are connected in series.

$R_{s_{2}}$ = R + R = 2R Ω

Now, $R_{s_{1}} + R_{s_{2}}$ + resistor 3 are connected in parallel.

$\dfrac{1}{R_p} = \dfrac{1}{2R} + \dfrac{1}{2R} + \dfrac{1}{2R}$

$\dfrac{1}{R_p} = \dfrac{3}{2R}$

$R_p = \dfrac{2R}{3} \Omega$

∴ $R_{eq} = \dfrac{2R}{3} \Omega$

Answer 2

$\sf R_1 + R_2 = 2R.........(R_a)$

$\sf R_4+R_5 = 2R.........(R_b)$

$\sf Total \: resistance(R_t) = R_a+R_b+R_3$

$\frac{1}{R_t} = \frac{1}{R_a} + \frac{1}{R_b} + \frac{1}{R_3}$

$\frac{1}{R_t=} = \frac{1}{2R} +\frac{1}{2R} + \frac{1}{2R}$

$\frac{1}{R_t} = \frac{3}{2R}$

$R_t= \frac{ 2R}{3}$