What is the value of equivalent resistance if the resistor 10 Ω is parallel to 20 Ω? 

The correct answer is option 3 i.e. 6.67Ω

Concept :

Resistance in Parallel :

• In this parallel connection, the end terminals of all resistances are connected to the same two nodes.
• The voltage drop across all resistances is the same.
• R_AB = R₁ || R₂ || R₃ ............... || R_n
• _{\(\frac{1}{R_{AB}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ................. + \frac{1}{R_{n}}\)}

Calculation :

Let R_AB is an equivalence resistance of 10 Ω and 20 Ω which is connected in parallel.

\(\frac{1}{R_{AB}} = \frac{1}{10} + \frac{1}{20}\)

R_AB = \(\frac{10 \times 20}{10 + 20}\) = 6.67Ω

Additional Information Resistance in Series:

• In this series connection, all resistances are connected in a single line by an end-to-end.
• The current is the same in all resistances.
• R_AB = R₁ + R₂ + R₃ + .................. + R_n