Question

When a certain wire is connected across a voltage of 1 V, the resulting current through the wire is 1 A. If we connect the same wire across a voltage of 2 V, the current will be

A 2A

B 4A

C 0.25A

D 1A

E 0.5A

Answer 1

Concepts and reason

The concept used to solve this problem is Ohm’s law.

Use Ohm’s law to find the current through the wire.

Fundamentals

Ohm’s law states that, “the potential difference across the conductor is proportional to the current through the conductor”.

The expression for the voltage is as follows:

$V = IR$

Here, the current is $I$, the voltage is $V$, and the resistance is $R$.

The incorrect options for current through the wire when the wire is connected across the voltage of $2\,{\rm{V}}$are given below:

• B) $4\,{\rm{A}}$

• C) $0.25\,{\rm{A}}$

• D) $1\,{\rm{A}}$

• E) $0.5\,{\rm{A}}$

The expression for the voltage is as follows:

$V = IR$ …… (1)

Rearrange the above expression for $R$.

$R = \frac{V}{I}$ …… (2)

When the wire is connected across the voltage of $1\,{\rm{V}}$, then the resistance of the wire is calculated as follows:

Substitute $1\,{\rm{V}}$ for $V$ and $1\,{\rm{A}}$ for $I$ in equation (2).

$\begin{array}{c}\\R = \frac{{1\,{\rm{V}}}}{{1\,{\rm{A}}}}\\\\ = 1\,\Omega \\\end{array}$

Rearrange the expression (1) for $I$.

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

When the wire is connected across the voltage of $2\,{\rm{V}}$, then the current through the wire is calculated as follows:

Substitute $2\,{\rm{V}}$ for $V$ and $1\,\Omega$ for $R$ in equation (2).

$\begin{array}{c}\\I = \frac{{2\,{\rm{V}}}}{{1\,\Omega }}\\\\ = 2\,{\rm{A}}\\\end{array}$

The correct option for the current through the wire when the wire is connected across the voltage of $2\,{\rm{V}}$ is given below:

• A) $2\,{\rm{A}}$

Therefore, the current through the wire when it is connected across the voltage of $2\,{\rm{V}}$is $2\,{\rm{A}}$.

Ans:

Thus, the current through the wire when it is connected across the voltage of ${\bf{2}}\,{\bf{V}}$is ${\bf{2}}\,{\bf{A}}$.