Chapter 23.2, Problem 27PP

To determine

The current through the blender.

Answer to Problem 27PP

  $1.13I_A$

Explanation of Solution

Given:

The resistance of the toaster, $R_1=15\Omega$

The resistance of the mixer, $R_2=25\Omega$

The resistance of the blender, $R_3=22\Omega$

Current through the mixer, $I_m=I_{\text{A}}$

Current through the blender, $I_b=I_{\text{B}}$

Formula used:

Ohm’s law,

  $V=IR$

Where, V is the voltage, I is the current and R is the resistance.

Calculation:

It is known that the potential difference remains same in parallel combination, thus voltage across blender will be same as that of the mixer. Hence,

  $\begin{array}{c}{V}_b=V_m\\ =I_{\text{A}}{R}_2\\ =25I_{\text{A}}\end{array}$

Then, the current through the blender will be,

  $\begin{array}{c}{I}_B=\frac{V_b}{R_b}\\ =\frac{25I_A}{22}\\ =1.13I_A\end{array}$

Conclusion:

Hence, the current through the blender is $1.13I_A$ .