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In a circuit with a 9V battery and two resistors of 3 ohms and 6 ohms in paralle
In a circuit with a 9V battery and two resistors of 3 ohms and 6 ohms in parallel, what is the equivalent resistance?
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Q1
In a circuit with a 9V battery and two resistors of 3 ohms and 6 ohms in parallel, what is the equivalent resistance?
2 ohms
3 ohms
4 ohms
1.5 ohms
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1/R_eq = 1/R1 + 1/R2 = 1/3 + 1/6 = 1/2, R_eq = 2 ohms.
Questions & Step-by-step Solutions
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Q
Q: In a circuit with a 9V battery and two resistors of 3 ohms and 6 ohms in parallel, what is the equivalent resistance?
Solution:
1/R_eq = 1/R1 + 1/R2 = 1/3 + 1/6 = 1/2, R_eq = 2 ohms.
Steps: 8
Show Steps
Step 1: Identify the resistors in the circuit. We have R1 = 3 ohms and R2 = 6 ohms.
Step 2: Use the formula for equivalent resistance in parallel circuits: 1/R_eq = 1/R1 + 1/R2.
Step 3: Substitute the values of R1 and R2 into the formula: 1/R_eq = 1/3 + 1/6.
Step 4: Find a common denominator to add the fractions. The common denominator for 3 and 6 is 6.
Step 5: Rewrite 1/3 as 2/6, so now we have: 1/R_eq = 2/6 + 1/6.
Step 6: Add the fractions: 1/R_eq = (2 + 1)/6 = 3/6.
Step 7: Simplify 3/6 to 1/2, so we have: 1/R_eq = 1/2.
Step 8: To find R_eq, take the reciprocal of 1/2: R_eq = 2 ohms.
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