Problem 3

A source with constant emf

E

and internal resistance

r>0

is connected to a resistive load

R>0

. Neglect lead resistance; let

I

be current,

U

the terminal and load voltage, and

P_R

the load power. (a) Find current. (b) Find load voltage. (c) Find load power and power lost inside the source. 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

\boxed{I=\frac{E}{R+r},\quad U=\frac{ER}{R+r},\quad P_R=\frac{E^2R}{(R+r)^2}}

problems.proof.analysis

Collect answers to every part, including signs, directions, and image or process properties where relevant. Dimensions match the physical quantities.