Understanding Resistance and Current Relationship

This question explores the relationship between electrical resistance, current, and voltage in a conductor. The key principle governing this relationship is Ohm's Law.

Applying Ohm's Law

Ohm's Law states that the voltage (\(V\)) across a conductor is directly proportional to the current (\(I\)) flowing through it, provided the temperature and other physical conditions remain unchanged. Mathematically, it is expressed as:

\( V = IR \)

Where:

• \(V\) is the voltage across the conductor (in Volts)
• \(I\) is the current flowing through the conductor (in Amperes)
• \(R\) is the resistance of the conductor (in Ohms)

In this problem, we are given that the voltage (\(V\)) remains constant.

Calculating the Impact of Increased Resistance

Let's denote the initial resistance as \(R_1\) and the initial current as \(I_1\). According to Ohm's Law:

\( V = I_1 R_1 \)

The problem states that the resistance is increased to three times its original value. Let the new resistance be \(R_2\). Therefore:

\( R_2 = 3 R_1 \)

Let the new current flowing through the conductor be \(I_2\). Since the voltage (\(V\)) remains constant, we can write the equation for the new state:

\( V = I_2 R_2 \)

Because the voltage \(V\) is constant in both situations, we can equate the two expressions:

\( I_1 R_1 = I_2 R_2 \)

Now, substitute the expression for \(R_2\) (\(R_2 = 3 R_1\)) into the equation:

\( I_1 R_1 = I_2 (3 R_1) \)

To find the new current (\(I_2\)), we can rearrange the equation. Assuming the initial resistance \(R_1\) is not zero, we can divide both sides by \(R_1\):

\( I_1 = 3 I_2 \)

Finally, solve for \(I_2\):

\( I_2 = \frac{I_1}{3} \)

Conclusion

The calculation shows that the new current (\(I_2\)) is one-third of the original current (\(I_1\)). Therefore, if the resistance of a conductor is increased to three times while the voltage remains constant, the current will become one third.