Question

Q) equivalent resistance of two resistors of 5 ohm & 10 ohm connected in parallel is equal to??

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 material and A = area of material.

R ∝ l

R ∝ ρ

R ∝ 1/A

Resistors can be connected in basically 2 ways:

1. Series Combination

2. Parallel Combination

Concept used: 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: Equivalent resistance of two resistors of 5 Ω and 10 Ω connected in parallel is equal to _____ .

Answer: Let R₁ = 5 Ω

R₂ = 10 Ω

They are connected in parallel.

$\dfrac{1}{R_{p}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}}$

$\dfrac{1}{R_{p}} = \dfrac{1}{5} + \dfrac{1}{10}$

$\dfrac{1}{R_{p}} = \dfrac{2 \: + \: 1}{10}$

$R_{p} = \dfrac{10}{3}$

$R_{p} = 3.33 \Omega$

∴ Equivalent resistance of two resistors of 5 Ω and 10 Ω connected in parallel is equal to 3.33  Ω.

Answer 2

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}

A

ρ∗l

where ρ = resistivity, l = length of material and A = area of material.

R ∝ l

R ∝ ρ

R ∝ 1/A

Resistors can be connected in basically 2 ways:

1. Series Combination

2. Parallel Combination

Concept used: In parallel combination,

Effective Resistance = R_{p}R

p

which is given by

\dfrac{1}{R_{p}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} + . . . + \dfrac{1}{R_{n}}

R

p

1

=

R

1

1

+

R

2

1

+...+

R

n

1

where n = number of resistors connected.

Given question: Equivalent resistance of two resistors of 5 Ω and 10 Ω connected in parallel is equal to _____ .

Answer: Let R₁ = 5 Ω

R₂ = 10 Ω

They are connected in parallel.

\dfrac{1}{R_{p}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}}

R

p

1

=

R

1

1

+

R

2

1

\dfrac{1}{R_{p}} = \dfrac{1}{5} + \dfrac{1}{10}

R

p

1

=

5

1

+

10

1

\dfrac{1}{R_{p}} = \dfrac{2 \: + \: 1}{10}

R

p

1

=

10

2+1

R_{p} = \dfrac{10}{3}R

p

=

3

10

R_{p} = 3.33 \text{\O}megaR

p

=3.33Ømega

∴ Equivalent resistance of two resistors of 5 Ω and 10 Ω connected in parallel is equal to 3.33 Ω.