In a circuit with a 5Ω and a 10Ω resistor in parallel, what is the total current if the voltage across them is 20V? (2022)

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Q: In a circuit with a 5Ω and a 10Ω resistor in parallel, what is the total current if the voltage across them is 20V? (2022)

Solution: First, find the equivalent resistance: 1/R_eq = 1/5 + 1/10 = 3/10, R_eq = 10/3Ω. Then, I = V/R_eq = 20V / (10/3)Ω = 6A.

Steps: 10

Step 1: Identify the resistors in the circuit. We have a 5Ω resistor and a 10Ω resistor in parallel.
Step 2: Use the formula for equivalent resistance in parallel: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values of the resistors into the formula: 1/R_eq = 1/5 + 1/10.
Step 4: Find a common denominator to add the fractions. The common denominator for 5 and 10 is 10.
Step 5: Rewrite the fractions: 1/5 = 2/10 and 1/10 = 1/10.
Step 6: Add the fractions: 1/R_eq = 2/10 + 1/10 = 3/10.
Step 7: Invert the result to find R_eq: R_eq = 10/3Ω.
Step 8: Use Ohm's Law to find the total current: I = V/R_eq.
Step 9: Substitute the voltage and equivalent resistance into the formula: I = 20V / (10/3)Ω.
Step 10: Simplify the calculation: I = 20V * (3/10) = 6A.