Chapter 4, Problem 1RQ

The current through a branch in a linear network is 2 A when the input source voltage is 10 V. If the voltage is reduced to 1 V and the polarity is reversed, the current through the branch is:

1. (a) –2 A
2. (b) –0.2 A
3. (c) 0.2 A
4. (d) 2 A
5. (e) 20 A

To determine

Choose the correct option to find the current through the branch when the polarity is reversed.

Answer to Problem 1RQ

The correct option from the given choices is $\left(\text{b}\right)-\text{0}\text{.2}\text{A}$.

Explanation of Solution

Given data:

The input voltage source is $10\text{V}$.

The current through the branch in a linear network is $2\text{A}$.

Calculation:

The circuit is a linear network, and the source voltage is reduced from $10\text{V}$ to $1\text{V}$ the value of current will also change due to the decrease in voltage.

The resistance of the branch calculated by using ohms law as follows,

$\begin{array}{c}R=\frac{10\text{V}}{2\text{A}}\\ =5\Omega \left\{\because 1\Omega =\frac{1\text{V}}{1\text{A}}\right\}\end{array}$

As the voltage is reduced to $1\text{V}$, the polarity is reversed $\left(-1\text{V}\right)$. Hence, the polarity of current is also changed.

Therefore, when the voltage is reduced $1\text{V}$ the new branch current is,

$\begin{array}{c}I=\left(\frac{-1\text{V}}{5\Omega }\right)\\ =-0.2\text{A}\left\{\because 1\text{A}=\frac{1\text{V}}{1\Omega }\right\}\end{array}$

The current through the branch when the polarity reversed is $-\text{0}\text{.2}\text{A}$. Therefore, the correct option is (b), and the options (a), (c), (d), and (e) are incorrect.

Conclusion:

Thus, the correct option from the given choices is $\left(\text{b}\right)-\text{0}\text{.2}\text{A}$.