Question

61. A network of five identical resistors, each of
value 25ohm is made as shown in the figure.
Equivalent resistance between points A and
Bis
(a) 125ohm
(b) 50ohm
(c) 25ohm
(d) 15ohm​

Answer 1

Solution :

⏭ Given:

✏ A network of five identical resistors, each of value 25Ω is made as shown in the figure.

⏭ To Find:

✏ Equivalent resistance between points A and B.

⏭ Concept:

✏ In this type of complex circuit question, first we have to simplify complex circuit diagram.

✏ For simplified circuit diagram, see the attachment.

✏ we can see the balanced wheat-stone bridge into simplified circuit diagram.

⏭ Calculation:

• Equivalent resistance of upper arm:

✏ R' = R1 + R3 (series connection)

✏ R' = 25 + 25

✏ R' = 50Ω

• Equivalent resistant of lower arm:

✏ R" = R2 + R4

✏ R" = 25 + 25

✏ R" = 50Ω

• Equivalent resistance between A and B :

✏ R = R'R"/R'R" (parallel connection)

✏ R = 2500/100

✏ R = 25Ω ✔

➡ Additional Information:

✏ For, balanced wheat-stone bridge the given condition is required

• R1/R2 = R3/R4

Answer 2

$\huge\underline{\underline{\bf \orange{Question-}}}$

A network of five identical resistors, each of value 25ohm is made as shown in the figure. Equivalent resistance between points A and B is

$\huge\underline{\underline{\bf \orange{Solution-}}}$

The given circuit forms a $\color{skyblue}\underline{\sf balanced\:Wheatstone\:bridge}$ between point A and B

See the Figure

The bridge is said to be balanced when deflection in galvanometer is zero. i.e ${\sf i_g=0}$ and hence ,

$\implies{\sf V_B=-V_D}$

Under this condition

$\implies{\sf V_A-V_B=V_A-V_D}$

$\implies{\sf i_1P=i_2R }$

$\color{darkblue}\implies{\sf \dfrac{i_1}{i_2}=\dfrac{R}{P}\:\:\:\;→(1) }$

Similarly ,

$\implies{\sf V_B-V_C=V_D-V_C}$

$\implies{\sf i_1Q=i_2S}$

$\color{darkblue}\implies{\sf \dfrac{i_1}{i_2}=\dfrac{S}{Q}\:\:\:\:→(2) }$

${\sf From\: Equation\:1\:and\:2-}$

$\color{red}\implies{\sf \dfrac{R}{P}=\dfrac{S}{Q} }$

Or

$\color{red}\implies{\sf \dfrac{P}{Q}=\dfrac{R}{S}}$

So, this is a condition for which a Wheatstone bridge is balanced .

━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore in this question ,

Answer will be $\color{red}\underline{\underline{\sf 25Ω }}$ because this is balanced wheatstone bridge between point A and B.