What is the equivalent resistance of a circuit with two 10Ω resistors in series and one 5Ω resistor in parallel with them?

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Q: What is the equivalent resistance of a circuit with two 10Ω resistors in series and one 5Ω resistor in parallel with them?

Solution: R_series = 10Ω + 10Ω = 20Ω. R_parallel = 1/(1/20 + 1/5) = 4Ω. Therefore, R_eq = 4Ω.

Steps: 8

Step 1: Identify the resistors in the circuit. We have two 10Ω resistors in series and one 5Ω resistor in parallel with them.
Step 2: Calculate the total resistance of the two 10Ω resistors in series. Add their resistances: 10Ω + 10Ω = 20Ω.
Step 3: Now, we have a 20Ω resistor (from Step 2) in parallel with the 5Ω resistor.
Step 4: Use the formula for resistors in parallel: R_parallel = 1 / (1/R1 + 1/R2). Here, R1 is 20Ω and R2 is 5Ω.
Step 5: Substitute the values into the formula: R_parallel = 1 / (1/20 + 1/5).
Step 6: Calculate 1/20 = 0.05 and 1/5 = 0.2. Now add them: 0.05 + 0.2 = 0.25.
Step 7: Take the reciprocal of 0.25 to find R_parallel: R_parallel = 1 / 0.25 = 4Ω.
Step 8: The equivalent resistance of the circuit is 4Ω.