If a circuit contains a 9V battery and three resistors (R1 = 3Ω, R2 = 3Ω, R3 = 3Ω) in parallel, what is the total current supplied by the battery?
Practice Questions
1 question
Q1
If a circuit contains a 9V battery and three resistors (R1 = 3Ω, R2 = 3Ω, R3 = 3Ω) in parallel, what is the total current supplied by the battery?
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The equivalent resistance for resistors in parallel is 1/R_total = 1/R1 + 1/R2 + 1/R3 = 1/3 + 1/3 + 1/3 = 1Ω. The total current is I = V/R_total = 9V / 1Ω = 9A.
Questions & Step-by-step Solutions
1 item
Q
Q: If a circuit contains a 9V battery and three resistors (R1 = 3Ω, R2 = 3Ω, R3 = 3Ω) in parallel, what is the total current supplied by the battery?
Solution: The equivalent resistance for resistors in parallel is 1/R_total = 1/R1 + 1/R2 + 1/R3 = 1/3 + 1/3 + 1/3 = 1Ω. The total current is I = V/R_total = 9V / 1Ω = 9A.
Steps: 9
Step 1: Identify the values given in the problem. We have a 9V battery and three resistors, each with a resistance of 3Ω (R1, R2, R3).
Step 2: Understand that the resistors are in parallel. This means we will use the formula for equivalent resistance in parallel circuits.
Step 3: Write the formula for equivalent resistance in parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3.
Step 4: Substitute the values of the resistors into the formula: 1/R_total = 1/3 + 1/3 + 1/3.
Step 5: Calculate the right side of the equation: 1/3 + 1/3 + 1/3 = 3/3 = 1.
Step 6: This means 1/R_total = 1, so R_total = 1Ω.
Step 7: Now, use Ohm's Law to find the total current supplied by the battery. The formula is I = V/R_total.
Step 8: Substitute the values into the formula: I = 9V / 1Ω.
