To determine the magnitude of the current in a series circuit containing two resistors, we need to follow these steps:
1. Determine the Total Resistance:
In a series circuit, the total resistance is the sum of the individual resistances. Given:
[tex]\[
\text{resistance1} = 10 \, \Omega
\][/tex]
[tex]\[
\text{resistance2} = 4 \, \Omega
\][/tex]
The total resistance [tex]\( R_{\text{total}} \)[/tex] is:
[tex]\[
R_{\text{total}} = 10 \, \Omega + 4 \, \Omega = 14 \, \Omega
\][/tex]
2. Use Ohm's Law to Find the Current:
Ohm’s Law is given by:
[tex]\[
V = I \times R
\][/tex]
This can be rearranged to solve for the current [tex]\( I \)[/tex]:
[tex]\[
I = \frac{V}{R}
\][/tex]
Given that the voltage [tex]\( V \)[/tex] is [tex]\( 42 \, \text{V} \)[/tex], and the total resistance [tex]\( R_{\text{total}} \)[/tex] is [tex]\( 14 \, \Omega \)[/tex], we can substitute these values into the equation:
[tex]\[
I = \frac{42 \, \text{V}}{14 \, \Omega} = 3 \, \text{A}
\][/tex]
Therefore, the magnitude of the current in the circuit is [tex]\( 3 \, \text{A} \)[/tex].
So, the best answer is [tex]\( \boxed{3 \, \text{A}} \)[/tex].
