Question

Which of the following would double the amount of current flowing through a piece of metal wire? Halve the voltage across it. Double the voltage across it. Quarter the voltage across it. Quadruple the voltage across it.

Answer 1

Concepts and reason

The concept used to solve this problem is ohm’s law because it gives a relation between voltage and current in a conductor. Verify how much change in the voltage would double the current flowing through a metal wire.

Fundamentals

Ohm’s law states that the current (i) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points.

$\begin{array}{l}\\{\rm{ }}V\alpha {\rm{ }}i\\\\V = iR\\\end{array}$

Here, R is the resistance of the conductor.

Rearrange the above equation for i.

$i = \frac{V}{R}$

The current (i) flowing through a piece of metal wire whose ends are placed between a potential difference (V) is,

$i = \frac{V}{R}$

Here, R is the resistance.

From above equation it is clear that the current in the metal wire is directly proportional to the voltage.

Half the voltage across the metal wire would half the current flowing through it.

Hence, half the voltage across the metal wire cannot double the current flowing through it.

Quarter the voltage across the metal wire would quarter the current flowing through it.

Hence, quarter the voltage across the metal wire cannot double the current flowing through it.

Quadruple the voltage across the metal wire would quadruple the current flowing through it.

Hence, quadruple the voltage across the metal wire cannot double the current flowing through it.

The current in the metal wire is directly proportional to the voltage. So to double the current in the metal wire voltage has to be doubled.

Hence, double the voltage would double the current flowing through a piece of metal wire.

Ans:

Double the voltage across the metal wire would double the current flowing through it.