Question

A circuit with a battery, a 10 Ω resistor, and a 11 Ω resistor, in parallel. The total current is the system is 4.4 A. What is the voltage of the battery?

Answer 1

Given data:

* The current through the circuit is,

`I=4.4\text{ A}`

* The value of resistances given is,

`\begin{gathered} R_1=10\text{ ohm} \\ R_2=11\text{ ohm} \end{gathered}`

Solution:

The equivalent resistance of the resistors connected in parallel is,

`\begin{gathered} (1)/(R_(eq))=(1)/(R_1)+(1)/(R_2) \\ (1)/(R_(eq))=(1)/(10)+(1)/(11) \\ (1)/(R_(eq))=(11+10)/(110) \\ (1)/(R_(eq))=(21)/(110) \end{gathered}`

By simplifying,

`\begin{gathered} R_(eq)=(110)/(21) \\ R_(eq)=5.24\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=4.4*5.24 \\ V=23.06\text{ volts} \end{gathered}`

Thus, the voltage across the battery is 23.06 volts.