Question

For both the questions .

Find the equivalent resistance between point X and Y .
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Answer 1

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{question \: no \: 1 \: = (d) \: 2r} \\ \\ \bf \: question \: no \: 2 = (c) \: \frac{8}{3} \omega$

$\bf{step \: by \: step \: explanation}$

1. equivalent resistance between x and y

°•° it is a parallel combination

•°• equivalent resistance

$\sf \implies \frac{ \large \: r \tiny1 \large r \tiny \: 2}{ \large \: r \tiny1 \large \: + \: r \tiny \: 2}$

For first parallel resistance

$\huge\sf \implies \: \frac{r \times r}{r + r}$

$\huge\sf \implies \: \frac{ {r}^{2} }{2r}$

→ similarly it will be for all .

On adding them we get

$\sf \implies \frac{ {r}^{2} }{2r} + \frac{ {r}^{2} }{2r} + \frac{ {r}^{2} }{2r} + \frac{ { r}^{2} }{2r} \\ \\ \sf \implies \frac{{4r}^{2} }{2r}$

$\huge \sf \implies \frac{ \cancel{ {4r}^{2} }}{ \cancel{2r}} = 2r$

2. equivalent resistance between x and y

°•° it is a parallel combination

•°• equivalent resistance

$\sf \implies \frac{ \large \: r \tiny1 \large r \tiny \: 2}{ \large \: r \tiny1 \large \: + \: r \tiny \: 2}$

For first resistance

$\huge\sf \implies\: \frac{4\times 2}{4+2}$

$\huge\sf \implies \: \frac{ 8}{6} = \frac{4}{3}$

similarly it will for second resistance

on adding them

$\huge\sf \implies \: \frac{ 4}{3} + \frac{4}{3} \\ \\ \huge\bf \implies \: \frac{ 8}{3} \omega$

Answer 2

Q. 1

Solution:

According to the question, it is a parallel commination.

By using the formula of equivalent resistance of parallel combination.

1/Rp = 1/R1 + 1/R2

=> R1 × R2 / R1 + R2

Substitute the values

=> R × R / R + R

=> R^2 / 2R

Now on adding,

=> R^2 / 2R + R^2 / 2R + R^2 / 2R + R^2 / 2R

=> 4R^2 / 2R = 2R

Therefore, Rp = 2R

Thus, the equivalent resistance between point X and Y is 2R.

Answer: (d). 2R

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Q. 2

Solution:

According to the question, it is a parallel commination.

By using the formula of equivalent resistance of parallel combination.

1/Rp = 1/R1 + 1/R2

=> R1 × R2 / R1 + R2

Substitute the values

For first resistance,

=> 4 × 2 / 4 + 2

=> 8 / 6 = 4 / 3 Ohm

Now on adding,

=> 4 / 3 + 4 / 3

=> 4 + 4 / 3

=> 8 / 3 Ohm.

Therefore, Rp = 8 / 3 Ohm.

Thus, the equivalent resistance between point X and Y is 8 / 3 Ohm.

Answer: (c). 8 / 3 Ohm.

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