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

I_1=V/R_1,\quad I_2=V/R_2

problems.proof.analysis

Apply the governing law for the stated model, using the sign convention in the problem. This provides the starting equation for the later parts.

problems.proof.pitfall. Do not add parallel resistances directly; add their reciprocals.