Question

A circuit with a battery, a 6 Ω resistor, a 21 Ω resistor, and a 27 Ω resistor in parallel. The total voltage is the system is 7.0 V. What is the total resistance of the circuit?

Answer 1

Given that the resistances are connected in parallel.

`\begin{gathered} R_1=6\text{ ohm} \\ R_2=21\text{ ohms} \\ R_3\text{ = 27 ohms} \end{gathered}`

Also, the total voltage is 7 V.

The formula to find the equivalent resistance connected in parallel is

`(1)/(R)=(1)/(R_1)+(1)/(R_2)+(1)/(R_3)`

Substituting the values, the resistance will be

`\begin{gathered} (1)/(R)=(1)/(6)+(1)/(21)+(1)/(27) \\ =(63+18+14)/(378) \\ =(95)/(378) \\ R=3.97\text{ ohm} \end{gathered}`

Thus, the total resistance of the circuit is 3.97 ohms.