Chapter 23, Problem 2STP

To determine

To Choose: The correct option.

Answer to Problem 2STP

Option D

Explanation of Solution

Given:

Value of resistance, $R_1=3.0\Omega$

Value of resistance, $R_2=12\Omega$

Value of resistance, $R_3=4.0\Omega$

Voltage of battery, $V=6.0\text{V}$

Formula used:

Equivalent resistance for parallel combination can be obtained by:

  $R_{eq}={\left[\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\right]}^{-1}$

Ohm’s law:

  $V=IR$

Here, I is the current, V is the potential difference and R is the resistance.

Calculations:

  $\begin{array}{c}{R}_{eq}={\left[\frac{1}{3.0}+\frac{1}{12}+\frac{1}{4.0}\right]}^{-1}\\ ={\left[\frac{4.0+1.0+3.0}{12}\right]}^{-1}\\ =1.5\Omega \end{array}$

Using Ohm’s law, calculate the current through the battery:

  $\begin{array}{l}V=I{R}_{eq}\\ I=\frac{6.0}{1.5}=4.0\text{A}\end{array}$

Conclusion:

Thus, the option D is correct.