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

ANSWER

$14V$

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:

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

Therefore, we have that:

$\begin{gathered} \frac{1}{R}=\frac{1}{4}+\frac{1}{10}=\frac{5+2}{20}=\frac{7}{20} \\ \Rightarrow R=\frac{20}{7}\Omega \end{gathered}$

Therefore, the voltage of the battery is:

$\begin{gathered} V=4.9\cdot\frac{20}{7} \\ V=14V \end{gathered}$

The voltage of the battery is 14V.