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In a circuit with a 20V battery and two resistors (4Ω and 8Ω) in parallel, what
In a circuit with a 20V battery and two resistors (4Ω and 8Ω) in parallel, what is the total current supplied by the battery?
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In a circuit with a 20V battery and two resistors (4Ω and 8Ω) in parallel, what is the total current supplied by the battery?
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Total resistance in parallel, 1/Req = 1/R1 + 1/R2 = 1/4 + 1/8 = 3/8. Therefore, Req = 8/3Ω. Total current I = V/Req = 20V / (8/3) = 7.5A.
Questions & Step-by-step Solutions
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Q
Q: In a circuit with a 20V battery and two resistors (4Ω and 8Ω) in parallel, what is the total current supplied by the battery?
Solution:
Total resistance in parallel, 1/Req = 1/R1 + 1/R2 = 1/4 + 1/8 = 3/8. Therefore, Req = 8/3Ω. Total current I = V/Req = 20V / (8/3) = 7.5A.
Steps: 9
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Step 1: Identify the values given in the problem. We have a 20V battery and two resistors: R1 = 4Ω and R2 = 8Ω.
Step 2: Understand that the resistors are in parallel. In parallel, the total resistance (Req) can be found using the formula: 1/Req = 1/R1 + 1/R2.
Step 3: Substitute the values of R1 and R2 into the formula: 1/Req = 1/4 + 1/8.
Step 4: Find a common denominator to add the fractions. The common denominator for 4 and 8 is 8. So, convert 1/4 to 2/8: 1/Req = 2/8 + 1/8.
Step 5: Add the fractions: 1/Req = (2 + 1)/8 = 3/8.
Step 6: To find Req, take the reciprocal of 3/8: Req = 8/3Ω.
Step 7: Now, use Ohm's Law to find the total current (I) supplied by the battery. The formula is I = V / Req.
Step 8: Substitute the values into the formula: I = 20V / (8/3).
Step 9: Simplify the division: I = 20V * (3/8) = 60/8 = 7.5A.
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