Question

In the network shown the equivalent resistance between P and Q is 4 /3 ohms.Hence the value of R is

Answer 1

Answer:

r =  6.2Ω

Step by step explanation:

As we can see from that diagram that the resistance 2Ω and 8Ω are parallel. Therefore, their equivalent resistance can be found as follows

$R_{eq1} =\frac{2\times8}{2+8}$

$R_{eq1} =\frac{16}{10}$

$R_{eq1} =1.6$

Similarly, we can see from that diagram that the resistance 6Ω and 4Ω are parallel. Therefore, their equivalent resistance can be found as follows

$R_{eq2}=\frac{6\times4}{6+4}$

$R_{eq2}=\frac{24}{10}$

$R_{eq2}=2.4$

Now , in our equivalent circuit $R_{eq1}$ and $R_{eq2}$ are in series, so the resultant resistance can be found as

$R_{eq}=R_{eq1}+R_{eq2}$

$R_{eq}=1.6+2.4$

$R_{eq}=4$

Now similarly, 3Ω and $R_{eq}$ are parallel, so their equivalent resitance can be found by the above process as well, which comes out to be

R = 1.76Ω

Now R and r are parallel and their equivalent resistance is equal to $\frac{4}{3}$

Using the above formula

$\frac{4}{3}=\frac{R\timesr}{R+r}$

$\frac{4}{3}=\frac{1.7\timesr}{1.7+r}$

cross multiplying

4(1.7 + r) = 3(1.7r)

6.8 + 4r = 5.1r

5.1r - 4r = 6.8

1.1r = 6.8

r =6.8÷1.1

r = 6.2Ω

Answer 2

Answer:

the ans is 6............