Question

A resistor of 8 Ω is connected in parallel with another resistor R₂. The resultant resistance of the combination is 4 Ω. Then, the value of resistor R₂ is:

• A. 12 Ω
• B. 4 Ω
• C. 8 Ω
• D. 16 Ω

Answer 1

The correct option is C

8 Ω

Given:
Equivalent resistance $R_{eq}=4\Omega$
Resistance of first resistor $R_1=8\Omega$
Resistance of second resistor $R_2=?$
equivalent resistance $R_{eq}=\frac{1}{R_1}+\frac{1}{R_2}$ or
$R_{eq}=\frac{R_1\times R_2}{R_1+R_2}$
$4=\frac{8\times R_2}{8+R_2}$
$\Rightarrow 32=4\times R_2$
$\therefore R_2=8\Omega$