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**Problem 5: Current, Energy and Power A battery of emf ε has internal resistance i R ,**

and let us suppose that it can provide the emf to a total charge Q before it expires.

Suppose that it is connected by wires with negligible resistance to an external (load) with

resistance L R .

a) What is the current in the circuit?

b) What value of L R maximizes the current extracted from the battery, and how

much chemical energy is generated in the battery before it expires?

c) What value of L R maximizes the total power delivered to the load, and how much

energy is delivered to the load before it expires? How does this compare to the

energy generated in the battery before it expires?

d) What value for the resistance in the load L R would you need if you want to

deliver 90% of the chemical energy generated in the battery to the load? What

current should flow? How does the power delivered to the load now compare to

the maximum power output you found in part c)?

and let us suppose that it can provide the emf to a total charge Q before it expires.

Suppose that it is connected by wires with negligible resistance to an external (load) with

resistance L R .

a) What is the current in the circuit?

b) What value of L R maximizes the current extracted from the battery, and how

much chemical energy is generated in the battery before it expires?

c) What value of L R maximizes the total power delivered to the load, and how much

energy is delivered to the load before it expires? How does this compare to the

energy generated in the battery before it expires?

d) What value for the resistance in the load L R would you need if you want to

deliver 90% of the chemical energy generated in the battery to the load? What

current should flow? How does the power delivered to the load now compare to

the maximum power output you found in part c)?

**2. Homework Equations**

Kirchoff's rules

V = IR

I = -dq/dt

Kirchoff's rules

V = IR

I = -dq/dt

**3. The Attempt at a Solution**

I'm assuming for part a, a simple use of Ohm's Laws would yield I = (Emf / (Ri + RL)

I don't know how to treat a battery that expires. Is there a set of equations for it? Or should I treat it was if it is a charged capacitor? Even if it is a charged capacitor I'm still a little clueless as to how to start this and what equations to use.

I'm assuming for part a, a simple use of Ohm's Laws would yield I = (Emf / (Ri + RL)

I don't know how to treat a battery that expires. Is there a set of equations for it? Or should I treat it was if it is a charged capacitor? Even if it is a charged capacitor I'm still a little clueless as to how to start this and what equations to use.