Question

Find the resistance between the points A &C.


Give an explained answer ​

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 two paths to flow.

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

(See the diagram attached.)

Two resistors of 2Ω and 2Ω are connected in series.

$R_{s_1}$ = 2 +2 = 4Ω

Now, 4Ω and 2Ω are connected in parallel.

$\dfrac{1}{R_p} = \dfrac{1}{4} + \dfrac{1}{2}$

$\dfrac{1}{R_p} = \dfrac{3}{4}$

$R_p = \dfrac{4}{3} \Omega$

Now, 2Ω, 4/3Ω and 2Ω are in series.

$R_{eq}$  = 2 + 2 + 4/3

$R_{eq} = \dfrac{16}{3} \Omega$

∴ $R_{eq}$ = 5.33 Ω

Answer 2

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