The figure below shows a portion of a circuit through which there is a current I

Question

The figure below shows a portion of a circuit through which there is a current I. The resistances are R1, R2, R3 and R4. What is the current i1 through resistor R1? (Use any variable or symbol stated above as necessary.) Must use only the variables in the question.

The figure below shows a portion of a circuit through which there is a current I. The resistances are R1, R2, R3 and R4. What is the current i1 through resistor R1? (Use any variable or symbol stated above as necessary.) Must use only the variables in the question.

Explanation / Answer

Combining R2, R3 and R4,

R=(R3+R4)*R2/(R2+R3+R4)

i1=IR/(R+R1)=(I*(R3+R4)*R2/(R2+R3+R4))/((R3+R4)*R2/(R2+R3+R4)+R1)

=I((R3+R4)*R2)/((R3+R4)*R2+R1(R2+R3+R4))=I(R2R3+R2R4)/(R2R3+R2R4+R1R2+R1R3+R1R4)

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