Answer:
False
Explanation:
The current flowing through a circuit can be computed by using Ohm's law:
[tex]I=\frac{V}{R_{eq}}[/tex]
where
V is the voltage of the battery
Req is the total resistance of the circuit
Let's now compare the two situations. Let's call R the resistance of each resistor (since they are identical, they have same resistance, R)
- Series configuration: in this case, the total resistance of the circuit is given by
[tex]R_{eq}=R+R=2R[/tex]
So the current through the circuit is
[tex]I_s=\frac{V}{2R}=\frac{1}{2}\frac{V}{R}[/tex] (1)
- Parallel configuration: in this case, the total resistance of the circuit is given by
[tex]\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}\\R_{eq}=\frac{R}{2}[/tex]
So the current through the circuit is
[tex]I_p=\frac{V}{R/2}=2\frac{V}{R}[/tex] (2)
By comparing (1) and (2), we see that the current in the parallel configuration is greater than in the series configuration:
[tex]I_p > I_s[/tex]
therefore, the correct answer is false.
