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

P_R=I^2R=\frac{E^2R}{(R+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. Do not equate emf E with load voltage U; internal resistance causes a drop Ir.