Parallel Circuit Current Division

Steps:

• Recognize two parallel branches: R1+R2 with current I1, R3+R4 with current I2, both across battery emf E.
• Apply Kirchhoff's voltage law: I1(R1 + R2) = I2(R3 + R4) = E.
• Total current I = I1 + I2.
• Derive current split: I2 = I × (R1 + R2) / [(R1 + R2) + (R3 + R4)], matching the normalized form in B.

Why B is correct:

• In parallel circuits, branch current is total current times the ratio of opposite branch resistance to total equivalent resistance, per Ohm's law and current division rule.

Why the others are wrong:

• A: Gives the expression for I1, not I2.
• C: Sums partial voltage drops across only R1 and R3, omitting R2 and R4.
• D: Adds full branch voltages, each equal to E, yielding 2E instead of E.

Final answer: B