Question

A wire of resistance 50 ohms is cut into 10 equal parts and then all the parts joined in parallel to each other to form a combination. Calculate the equivalent resistance of the combination.

Answer 1

Answer

Eq. Resistance = 0.5 Ω

Given

A wire of resistance 50 ohms is cut into 10 equal parts and then all the parts joined in parallel to each other to form a combination

To Find

Equivalent resistance of the combination

Solution

__________

_ _ _ _ _ _ _ _ _ _

As we all know that , length is directly proportional to the resistance .

So , when the wire is cut into 10 equal parts ,

Resultant resistance of the new part is R/₁₀ .

When these 10 parts are connected in parallel .$\to \rm \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+.....+\dfrac{1}{R_{10}}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{1}{(R/10)}+\dfrac{1}{(R/10)}+.....+\dfrac{1}{(R/10)}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{10}{R}+\dfrac{10}{R}+.....+\dfrac{10}{R}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{100}{R}\\\\\to \rm R_{eq}=\dfrac{R}{100}$

Given , Resistance of the wire is 50 Ω .

$\to \rm R_{eq}=\dfrac{50}{100}\\\\\to \rm R_{eq}=\dfrac{1}{2}\\\\\to \bf R_{eq}=0.5\ \Omega\ \; \pink{\bigstar}$

Answer 2

Answer:

Answer

Eq. Resistance = 0.5 Ω

Given

A wire of resistance 50 ohms is cut into 10 equal parts and then all the parts joined in parallel to each other to form a combination

To Find

Equivalent resistance of the combination

Solution

__________

_ _ _ _ _ _ _ _ _ _

As we all know that , length is directly proportional to the resistance .

So , when the wire is cut into 10 equal parts ,

Resultant resistance of the new part is R/₁₀ .

When these 10 parts are connected in parallel .\begin{gathered}\to \rm \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+.....+\dfrac{1}{R_{10}}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{1}{(R/10)}+\dfrac{1}{(R/10)}+.....+\dfrac{1}{(R/10)}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{10}{R}+\dfrac{10}{R}+.....+\dfrac{10}{R}\\\\\to \rm \dfrac{1}{R_{eq}}=\dfrac{100}{R}\\\\\to \rm R_{eq}=\dfrac{R}{100}\end{gathered}

→

R

eq

1

=

R

1

1

+

R

2

1

+.....+

R

10

1

→

R

eq

1

=

(R/10)

1

+

(R/10)

1

+.....+

(R/10)

1

→

R

eq

1

=

R

10

+

R

10

+.....+

R

10

→

R

eq

1

=

R

100

→R

eq

=

100

R

Given , Resistance of the wire is 50 Ω .

\begin{gathered}\to \rm R_{eq}=\dfrac{50}{100}\\\\\to \rm R_{eq}=\dfrac{1}{2}\\\\\to \bf R_{eq}=0.5\ \text{\O}mega\ \; \pink{\bigstar}\end{gathered}

→R

eq

=

100

50

→R

eq

=

2

1

→R

eq

=0.5 Ømega ★