Answer to Question #263775 in Physics for RAFAEL

Question

A 10Ω resistor is connected in parallel to 32Ω resistor and a voltage source of 24V. Find the effective resistance and total current provided in the circuit. Determine the current in each of the resistors.

Answer 1

Let's first find the effective resistance in case of the parallel connection of resistors:

$$R_e=\dfrac{R_1R_2}{R_1+R_2}=\dfrac{32\ \Omega\times10\ \Omega}{32\ \Omega+10\ \Omega}=7.62\ \Omega.$$

Then, we can find the total current in the circuit as follows:

$$I=\dfrac{V}{R_e}=\dfrac{24\ V}{7.62\ \Omega}=3.15\ A.$$

We can find the current in each of the resistors as follows:

$$I_1=\dfrac{V}{R_1}=\dfrac{24\ V}{32\ \Omega}=0.75\ A,$$ $$I_2=\dfrac{V}{R_2}=\dfrac{24\ V}{10\ \Omega}=2.4\ A.$$