Question

A cell gives a balance with 85cm of a potentiometer wire. When the terminals of the cell are shorted through a resistance of 7.5 ohm, the balance point obtained at 75cm. Find the internal resistance of the cell​

Answer 1

Answer :-

$\implies \boxed{ \sf{ r = 1\:\Omega }}$

To Find :-

→Internal resistance of the cell .

Explanation :-

Given that

$\star \: \red{ \sf{ length \: L_{1} =} \green{85 \: cm \: }} \: \\ \star \sf{ \pink{ balance \: point \: }obtain \: at \: }\\ \: \: \: \sf{L_{2} \: = 75 \: cm \: } \\ \star \: \sf{ \green{Resistance (R) } \: = 7.5 \: \Omega \: } \\ \star \: \sf{internal \: \red{ resistance \: (r) = ? } \: }$

We know that

$\implies \sf{internal \: \green{ resistance \: (r)} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\sf{r \: = R \bigg( \red{\: \frac{L_{1} }{L_{2} } - 1} \bigg)}}$

substitute the given values .

$\implies \sf{r = 7.5 \bigg( \frac{85}{75} - 1 \bigg)} \\ \\ \implies \sf{ \: r = 7.5 \bigg( \frac{85 - 75}{75} \bigg)} \\ \\ \implies \sf{r = 7.5 \times \frac{10}{75} } \\ \\ \implies \sf{ r=\frac{ \red{\cancel{ \green{75}}}}{ \cancel{10}} \times \: \frac{ \cancel{10}}{ \red{ \cancel{ \green{75}}}} } \: \\ \\ \implies \boxed{ \sf{ r = 1\:\Omega}}$

hence ,its internal resistance is 1 ohm .

Answer 2

$\tt{\huge{\orange { ----------- }}}$

QUESTION :

A cell gives a balance with 85cm of a potentiometer wire.

When the terminals of the cell are shorted through a resistance of 7.5 ohm, the balance point obtained at 75cm.

Find the internal resistance of the cell.

SOLUTION :

We have the following information given :

The required cell gives a balance with 85cm of a potentiometer wire.

So , Length of wire for Balance Point 1 = 85 cm.

When the terminals of the cell are shorted through a resistance of 7.5 ohm, the balance point obtained at 75cm.

So , length of wire required for Balance Point 2 = 75 cm.

We know the following formula :

R _ { Internal } = r [ { L 1 - L 2} / { L2} ]

=> R _ { Internal } = 7.5 × { 10 / 75 } = 1

=> R _ { Internal } = 1

Hence the internal resistance of the required cell is I Ohm.

ANSWER :

The internal resistance of the cell is 1 Ohm.