Question

A circuit with a battery, a 14 Ω resistor, and a 17 Ω resistor, in parallel. The total current is the system is 2.8 A. What is the voltage of the battery?

Answer 1

Given data:

* The total current in the system is I = 2.8 A.

* The resistance of resistors connected in parallel is,

`\begin{gathered} R_1=14\text{ ohm} \\ R_2=17\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)/(14)+(1)/(17) \\ (1)/(R_(eq))=(17+14)/(14*17) \\ R_(eq)=(14*17)/(17+14) \\ R_(eq)=7.68\text{ ohm} \end{gathered}`

According to Ohm's law, the voltage across the battery in terms of the current and equivalent resistance is,

`\begin{gathered} V=IR_(eq) \\ V=2.8*7.68 \\ V=21.5\text{ volts} \end{gathered}`

Thus, the voltage across the battery is 21.5 volts.