Question

Choose true or false for each statement regarding the resistance of a wire.

true false While maintaining a constant voltage V, the current I increases when the cross-sectional area A of a wire expands.
true false While maintaining a constant voltage V, the current I increases when the resistivity rho of a wire decreases.
true false The resistivity rho is proportional to the resistance R of a wire.

Tries 0/2

Choose true or false for each statement regarding resistors in a circuit.
true false If you connect two different resistors in series in a circuit, then the current that flows through each of them is different.
true false Three identical resistors in series have one third the resistance of each individual one.
true false If you connect two different resistors in series in a circuit, then the voltage across each of them is the same.

Answer 1

Please see below as the answers are self-explanatory.

Step-by-step explanation:

1) True

• The resistance of a wire, can be expressed as follows:

`R =\rho*(L)/(A) (1)`

• So, if A increases, the resistance R decreases.
• Assuming that the wire is in the linear region of operation, we can apply to it Ohm's Law, as follows:

`V = I*R`

• So, if V= constant, and R decreases, I must be larger.

2) True

• If the resistivity ρ decreases, from (1) we conclude that R decreases.

• So, if V= constant, and R decreases, I must be larger.

3) True

• From (1) we can see that there exists a direct proportionality between the resistance of the wire and the resistivity.

4) False

• Two elements are connected in series, when the current flowing through them is the same.

5) False

• The equivalent resistance of three identical resistors, connected in series, is three times the resistance of any of them.

6) False

• In a series circuit, as the current I is the same, applying Ohm's law, the voltage V between terminals of any element is as follows:

`V = I*R`

• So, if I is the same, and R is different, the voltage across them will never be the same.