Question

A circuit with a battery, a 4 Ω resistor, and a 10 Ω resistor, in parallel. The total current is the system is 4.9 A. What is the voltage of the battery?

Answer 1

`14V`

Step-by-step explanation

We want to find the voltage of the battery.

To do this, we apply the relationship between voltage and current using Ohm's law:

`V=IR`

where R = resistance

I = current

The resistance is the total resistance of the circuit. Since the resistors are in parallel, the total resistance is found by using:

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

Therefore, we have that:

`\begin{gathered} (1)/(R)=(1)/(4)+(1)/(10)=(5+2)/(20)=(7)/(20) \\ \Rightarrow R=(20)/(7)\Omega \end{gathered}`

Therefore, the voltage of the battery is:

`\begin{gathered} V=4.9\cdot(20)/(7) \\ V=14V \end{gathered}`

The voltage of the battery is 14V.