If the current in a circuit is split into two branches with resistances R1 = 2Ω and R2 = 4Ω, what is the current through R1 if the total current is 6A?
Practice Questions
1 question
Q1
If the current in a circuit is split into two branches with resistances R1 = 2Ω and R2 = 4Ω, what is the current through R1 if the total current is 6A?
2A
3A
4A
6A
Using the current division rule, I1 = I_total * (R2 / (R1 + R2)) = 6A * (4Ω / (2Ω + 4Ω)) = 6A * (4/6) = 4A.
Questions & Step-by-step Solutions
1 item
Q
Q: If the current in a circuit is split into two branches with resistances R1 = 2Ω and R2 = 4Ω, what is the current through R1 if the total current is 6A?
Solution: Using the current division rule, I1 = I_total * (R2 / (R1 + R2)) = 6A * (4Ω / (2Ω + 4Ω)) = 6A * (4/6) = 4A.
Steps: 8
Step 1: Identify the total current in the circuit, which is given as 6A.
Step 2: Identify the resistances of the two branches: R1 = 2Ω and R2 = 4Ω.
Step 3: Use the current division rule formula: I1 = I_total * (R2 / (R1 + R2)).
Step 4: Substitute the values into the formula: I1 = 6A * (4Ω / (2Ω + 4Ω)).
Step 5: Calculate the total resistance in the denominator: 2Ω + 4Ω = 6Ω.
Step 6: Substitute this value back into the formula: I1 = 6A * (4Ω / 6Ω).
Step 7: Simplify the fraction: 4Ω / 6Ω = 2/3.
Step 8: Multiply the total current by the simplified fraction: I1 = 6A * (2/3) = 4A.
