Physics: In a circuit, two identical resistances are connected, first in series and then in parallel. the circuit will draw greater current in the first case. true or false?

In a circuit, two identical resistances are connected,

levilugar

13.01.2022

False

Explanation:

The current flowing through a circuit can be computed by using Ohm's law:

$I=\frac{V}{R_{eq}}$

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

$R_{eq}=R+R=2R$

So the current through the circuit is

$I_s=\frac{V}{2R}=\frac{1}{2}\frac{V}{R}$ (1)

- Parallel configuration: in this case, the total resistance of the circuit is given by

$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}\\R_{eq}=\frac{R}{2}$

So the current through the circuit is

$I_p=\frac{V}{R/2}=2\frac{V}{R}$ (2)

By comparing (1) and (2), we see that the current in the parallel configuration is greater than in the series configuration:

I_p I_s

therefore, the correct answer is false.

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