Solving Resistance of a Wire: 21V Across 32m, 18m?

[john216]

Homework Statement

Suppose that a 32-meter length of resistive wire is connected across the terminals of a battery. If a voltmeter reads 21 V when connected across the battery terminals, what should it read when connected across a 18-meter section of the wire? Enter you answers using one decimal place, do not enter units.

Homework Equations

e = iR

The Attempt at a Solution

thought the voltage doesn't change.
but I think its wrong. Please help?

 

[SammyS]

Homework Statement

Suppose that a 32-meter length of resistive wire is connected across the terminals of a battery. If a voltmeter reads 21 V when connected across the battery terminals, what should it read when connected across a 18-meter section of the wire? Enter you answers using one decimal place, do not enter units.

Homework Equations

e = iR

The Attempt at a Solution

thought the voltage doesn't change.
but I think its wrong. Please help?

Hello john216. Welcome to PF !

Think of this as 32 one-meter lengths of wire connected in series.

What is the voltage drop across anyone of those one-meter wires ?

How much across 18 of them ?

 

[john216]

could you clarify little?
i'm confused

 

[SammyS]

could you clarify little?
I'm confused

It's hard for me to know what part/parts of what I posted confuses you.

What do you understand about series circuits and resistances in series?

What do you understand about voltage drop and Ohm's Law?

etc.

 

[asteriatic]

I would like to clarify some information before providing a response. Is the resistive wire connected in series or parallel with the battery? Is the wire a uniform material or does it vary in composition along its length? Without this information, it is difficult to accurately determine the voltage reading when connected across a shorter section of the wire.

However, assuming the wire is connected in series with the battery and is a uniform material, the voltage reading across the 18-meter section of the wire would be 15.75 V. This can be calculated using Ohm's Law, where voltage (V) is equal to current (I) multiplied by resistance (R). Since the voltage remains constant in a series circuit, the current flowing through the wire would also remain constant. Therefore, the resistance of the 18-meter section of the wire can be calculated by dividing the voltage (21 V) by the current (which remains the same) and multiplying by the length (18 m). This results in a resistance of 12.6 ohms.

If the wire was connected in parallel with the battery, the voltage reading across the 18-meter section would be the same as the battery voltage (21 V). This is because in a parallel circuit, the voltage remains the same across all components.

However, if the wire is not a uniform material or there are other factors at play, the voltage reading may be different. It is important to consider all variables and information when solving for resistance in a circuit.