Answer to Question #263775 in Physics for RAFAEL

Question #263775

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.

1
Expert's answer
2021-11-10T10:09:08-0500

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


Re=R1R2R1+R2=32 Ω×10 Ω32 Ω+10 Ω=7.62 Ω.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=VRe=24 V7.62 Ω=3.15 A.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:


I1=VR1=24 V32 Ω=0.75 A,I_1=\dfrac{V}{R_1}=\dfrac{24\ V}{32\ \Omega}=0.75\ A,I2=VR2=24 V10 Ω=2.4 A.I_2=\dfrac{V}{R_2}=\dfrac{24\ V}{10\ \Omega}=2.4\ A.

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