High School

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A series circuit contains three [tex]2 \, \Omega[/tex] resistors and a [tex]6 \, \Omega[/tex] resistor. The current in each resistor is [tex]4.0 \, A[/tex].

What is the voltage of the battery in the circuit?

A. 2.0 V
B. 3.0 V
C. 32 V
D. 48 V

Answer :

First, recognize that in a series circuit the total resistance is the sum of all individual resistances. The circuit has three resistors of [tex]\(2\,\Omega\)[/tex] each and one resistor of [tex]\(6\,\Omega\)[/tex]. So, the total resistance [tex]\( R_{\text{total}} \)[/tex] is:

[tex]$$
R_{\text{total}} = 2\,\Omega + 2\,\Omega + 2\,\Omega + 6\,\Omega = 12\,\Omega.
$$[/tex]

Since the current [tex]\( I \)[/tex] in the circuit is given as [tex]\(4.0\,\text{A}\)[/tex], we use Ohm's law, which states:

[tex]$$
V = I \times R.
$$[/tex]

Substituting the known values:

[tex]$$
V = 4.0\,\text{A} \times 12\,\Omega = 48\,\text{V}.
$$[/tex]

Thus, the voltage of the battery is:

[tex]$$
\boxed{48\,\text{V}}.
$$[/tex]

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