Problem 3

Two positive resistors

R_1,R_2

are connected in parallel across an ideal constant voltage source

V>0

; neglect lead resistance. Let

I_1,I_2

be branch currents,

I

the total current, and

R_{eq}

the equivalent resistance. (a) Find

R_{eq}

and

I

. (b) Find total power and power in each resistor. (c) For

R_1=R_2=R

, compare equivalent resistance with

R

and total current with one branch current. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

R_{eq}=R_1R_2/(R_1+R_2)

problems.proof.analysis

Solve the algebraic expression and retain the solution consistent with the physical domain. Checking units helps catch algebraic errors.

problems.proof.pitfall. Parallel resistances combine by reciprocals; branch voltages, not currents, are equal.