Question

Part A

If the voltage across a circuit of constant resistance is doubled, how is the current in the circuit affected? If the voltage across a circuit of constant resistance is doubled, how is the current in the circuit affected?

1-The current is reduced by a factor of 4.

2-The current is doubled.

3- The current is reduced by a factor of 2.

4-The current remains constant.

5-The current is quadrupled.

Answer 1

Concept and reason

The concept required to solve this question is Ohm’s law.

First, write the expression for the new current in the circuit by using the Ohm’s law. Finally, determine the variation of the current in the circuit with voltage.

Fundamentals

According to ohm’s law, the current in the circuit is directly proportional to the voltage across a circuit.

$V \propto i$

The expression for the voltage across the circuit is,

$V = iR$

Here, $V$ is the voltage across the circuit, $i$ is current in the circuit, and $R$ is the resistance of the material.

(A)

The relation between voltage and current is,

$V = iR$

The relation between the initial voltage ${V_1}$ across the circuit and the initial current ${i_1}$ in the circuit when the resistance remains constant is,

${V_1} = {i_1}R$

The relation between the final voltage ${V_2}$ across the circuit and the final current ${i_2}$ in the circuit when the resistance remains constant is,

${V_2} = {i_2}R$

Solve the above two equations for the new current ${i_2}$ in the circuit.

$\begin{array}{c}\\\frac{{{V_2}}}{{{V_1}}} = \frac{{{i_2}R}}{{{i_1}R}}\\\\\frac{{{V_2}}}{{{V_1}}} = \frac{{{i_2}}}{{{i_1}}}\\\\{i_2} = \left( {\frac{{{V_2}}}{{{V_1}}}} \right){i_1}\\\end{array}$

The expression for the current ${i_2}$ in terms of current ${i_1}$ is,

${i_2} = \left( {\frac{{{V_2}}}{{{V_1}}}} \right){i_1}$

Given that, the voltage across the circuit is doubled, that is ${V_2} = 2{V_1}$ .

Substitute $2{V_1}$ for ${V_2}$ in equation ${i_2} = \left( {\frac{{{V_2}}}{{{V_1}}}} \right){i_1}$ .

$\begin{array}{c}\\{i_2} = \left( {\frac{{2{V_1}}}{{{V_1}}}} \right){i_1}\\\\ = 2{i_1}\\\end{array}$

Ans: Part A

The current is doubled when the voltage across the circuit is doubled.