Lesson 4 + 5 + 7

Question 1

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What is the maximum power a battery can deliver to a customer for a short time?

Answer 1

The maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source!

Question 2

Formel kinetische Energie

Answer 2

E = 1/2 * m * v^2

Question 3

Formel potenzielle Energie

Answer 3

E = m * g * h

Question 4

Capacitance of capacitor:

Answer 4

Question 5

Capacitor KUH = KUH

Answer 5

Q = C * U

Question 6

Energy of capacitor:

Answer 6

E = 1/2 * C * U^2

Question 7

Electrical field of Capacitor

Answer 7

E_E = U / d

Question 8

Charge density (surface Area) Capacitor

Answer 8

sigma =Q / A

Question 9

Formula for discharge at Capacitor

Answer 9

Question 10

(Simplified) equivalent circuit diagram of a (super-) capacitor

Answer 10

Question 11

The open circuit voltage of a supercapacitor is not constant. What effects occur
inside the capacitor that lead to a change of the voltage? What effect occurs if
the SuperCap is charged to too high voltages?

Answer 11

Decrease of the open-circuit voltage 𝑈0

Porosity of the electrodes leads to charges being distributed within the pores of the electrode material. Theoretically, no charges are lost (no change in state of charge). Macroscopically, however, a voltage drop can be observed.

Self-discharge occurs because of charges leaving the capacitor on parasitic ways. This form of self-discharge occurs permanently and is due to the humidity of the air or the surface conductivity of the insulators.

If a supercap is charged to an overvoltage (U > 𝑈𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛), ageing
processes such as the decomposition of the electrolyte are accelerated.

Question 12

Typical energy density of a supercap

Answer 12

3 Wh/kg

Too low to serve as energy storage for an EV

Question 13

What are typical applications of SuperCaps in vehicles? What are typical
storage capacities for those applications?

Answer 13

Use cases of supercapacitors:

 Voltage stabilization in car electronics (e.g. radio) ~ 1 - 2 Farad

 Recuperation of braking energy ~ 5 - 5000 Farad

 Automatic start-stop system

 Acceleration support in hybrid vehicles

Question 14

Self-inductance of a long coil

Answer 14

Question 15

Induced voltage in coil

Answer 15

Question 16

Amount of energy stored in a coil

Answer 16

E = 1/2 * L * I^2

Question 17

Describe the general design of flywheels. Which different types of flywheels
exist and to what extend do they differ from one another? Which components
cause the highest losses and self-discharge?

Answer 17