Question

A circuit with a battery, a 3 Ω resistor, and a 15 Ω resistor, in parallel. The total current is the system is 3.0 A. What is the voltage of the battery?

Answer 1

Given data:

* The current through the system is I = 3 A.

* The resistance of resistors connected in parallel is,

`\begin{gathered} R_1=3\text{ ohm} \\ R_2=15\text{ ohm} \end{gathered}`

Solution:

The equivalent resistance of the system is,

`(1)/(R_(eq))=(1)/(R_1)+(1)/(R_2)`

Substituting the known values,

`\begin{gathered} (1)/(R_(eq))=(1)/(3)+(1)/(15) \\ (1)/(R_(eq))=(5+1)/(15) \\ (1)/(R_(eq))=(6)/(15) \end{gathered}`

By taking inverse value,

`\begin{gathered} R_(eq)=(15)/(4) \\ R_(eq)=3.75\text{ ohm} \end{gathered}`

According to Ohm's law, the voltage across the battery is,

`V=IR_(eq)`

Substituting the known values,

`\begin{gathered} V=3*3.75 \\ V=11.25\text{ volts} \end{gathered}`

Thus, the voltage across the battery is 11.25 volts.