The voltage measured across the resistance [tex]R_{2}[/tex] will be [tex]\boxed{3\text{ V}}[/tex].
Explanation:
The two resistances in the given circuit are connected end to end. This connection of the resistors is termed as the series connection of the resistance.
Write the expression for the equivalent resistance of the two resistors.
[tex]R_{eq}=R_{1}+R_{2}[/tex]
Substitute the value of resistance in equation.
[tex]\begin{aligned}R_{eq}&=3\,\Omega+3\,\Omega\\&=6\,\Omega\end{aligned}[/tex]
Since the two batteries are connected in series. So the net voltage in the circuit will be [tex]6\text{ V}[/tex].
Write the expression for the total current drawn from the voltage source.
[tex]\boxed{I=\dfrac{V}{R}}[/tex]
Substitute the values of voltage drop and the total resistance in above expression.
[tex]\begin{aligned}I&=\dfrac{6}{6}\text{ A}\\&=1\text{ A}\end{aligned}[/tex]
The current in a series circuit remains constant through all the elements. Therefore, the current through each resistor will be [tex]1\text{ A}[/tex].
Write the expression for the voltage across the resistance [tex]R_{2}[/tex].
[tex]V'=I\times{R_{2}}[/tex]
Substitute the value of resistance and current in above expression.
[tex]\begin{aligned}V'&=(1\text{ A})\times(3\,\Omega)\\&=3\text{ V}\end{aligned}[/tex]
Thus, the voltage measured across the resistance [tex]R_{2}[/tex] will be [tex]\boxed{3\text{ V}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Electric Current
Keywords:
circuit, resistance, current, voltage drop, potential difference, measure across, equal resistance, current drawn.
