Question

The equivalent resistance of two resistors connected in series is $6\, \Omega$ and their parallel equivalent resistance is $\frac{4}{3} \Omega$. What are the values of resistances ?

• A. $4 \Omega, 6 \Omega$
• B. $8 \Omega , 1 \Omega$
• C. $4 \Omega , 2 \Omega$
• D. $6 \Omega, 2 \Omega$

Answer 1

Answer: (C)

$4 \Omega , 2 \Omega$

Answer 2

Let the value of resistance be $R_{1}$ and $R_{2}$ respectively. When $R_{1}$ and $R_{2}$ resistances are in series So, $R_{1}+R_{2}=6 \Omega\,\,\,\,\,\dots(i)$ (According to the question) When $R_{1}$ and $R_{2}$ resistances are in parallel So, $\frac{R_{1} R_{2}}{R_{1}+R_{2}}=\frac{4}{3} \Omega\,\,\,\,\, \dots(ii)$ From the E (i), we get $\frac{R_{1} R_{2}}{6}=\frac{4}{3}$ $R_{1} R_{2}=4 \times 2$ $R_{1} R_{2}=8\,\,\,\,\,\dots(iii)$ We know that $R_{1}-R_{2} =\sqrt{\left(R_{1}+R_{2}\right)^{2}-4 R_{1} R_{2}}$ $=\sqrt{36-4 \times 8}$ $R_{1}-R_{2} =\sqrt{4}$ $R_{1}-R_{2} =2 \Omega\,\,\,\,\,\dots(iv)$ From the Eqs. (i) and (iv), we get $R_{1}=4 \Omega, R_{2}=2 \Omega$