Question

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?

Answer 1

False

Step-by-step explanation:

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

`I=(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=(V)/(2R)=(1)/(2)(V)/(R)` (1)

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

`(1)/(R_(eq))=(1)/(R)+(1)/(R)=(2)/(R)\\R_(eq)=(R)/(2)`

So the current through the circuit is

`I_p=(V)/(R/2)=2(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.