Question

Consider three resistors with unequal resistances connected in series to a battery. Which of the following statements are true? Check all that apply.

The algebraic sum of the voltages across the three resistors is equal to the voltage supplied by the battery.

The current flowing through each of the resistors is the same and is equal to the current supplied by the battery.

The equivalent resistance of the combination of resistors is greater than the resistance of any one of the three resistors.

The algebraic sum of the currents flowing through each of the three resistors is equal to the current supplied by the battery.

The equivalent resistance of the combination of resistors is less than the resistance of any one of the three resistors.

The voltage across each of the resistors is the same and is equal in magnitude to the voltage of the battery.

Answer 1

Statements 1,2,3 are true

Step-by-step explanation:

First of all, let's remind the definition of resistances connected in series:

- Resistors are said to be connected in series when they are connected along the same branch, so that the same current flows through them, and the equivalent resistance of the combination is equal to the sum of the individual resistances:

`R_(eq)=R_1 + R_2 + ... +R_n`

Let's now analyze each statement:

1- The algebraic sum of the voltages across the three resistors is equal to the voltage supplied by the battery. --> TRUE. Since the resistors are connected along the same branch, the total voltage supplied by the battery is equal to the sum of the voltages across each resistor.

2- The current flowing through each of the resistors is the same and is equal to the current supplied by the battery. --> TRUE. As stated in the definition above, the current through each resistor is the same, since the resistors are connected along the same branch.

3- The equivalent resistance of the combination of resistors is greater than the resistance of any one of the three resistors. --> TRUE. As we said above, the equivalent resistance is equal to the sum of the individual resistances:

`R_(eq)=R_1 + R_2 + ... +R_n`

So, the equivalent resistance is always greater than the individual resistances.

4- The algebraic sum of the currents flowing through each of the three resistors is equal to the current supplied by the battery. --> FALSE. In fact, the current is the same through each resistor, and the value of the current is equal to the current erogated from the battery.

5- The equivalent resistance of the combination of resistors is less than the resistance of any one of the three resistors. --> FALSE. This is in contradiction with statement #3, so it is wrong.

6- The voltage across each of the resistors is the same and is equal in magnitude to the voltage of the battery. --> FALSE. This is in contradiction with #1, so it is wrong.