Title: 2.3 Exercise - Power and Energy

Question 1

Q: Accidentally, you forgot to turn off the 50-Watt light bulb in the basement and, thus, it was on for two days. How much did this oversight cost, if electricity costs 20 cents/kWh?

[...] cents
A: 48

Given information:

- Power: p = 40 Watt
- Time: t = 2 days = 48h
- Cost of electricity: c = 20 ct/kWh

Total energy consumed: E = p * t = 500 W * 48 h = 2400 Wh = 2.4 kWh

Total cost: c_tot = c * E = 20 ct/kWh * 2.4 kWh = 48 cents

Question 2

Q: An electric oven carries a current of 20 A at a voltage of 230 V. The oven is operated for two hours.

      a. What is the charge (in Coulombs) that passes through the oven? [...] kC

     b. What is the power absorbed by the oven? [...] kW

     c. What is the cost of operating the oven for two hours if electricity costs 20 cents/kWh? [...] cents
A: 144; 4.6/4,6; 184

Given information:

- Current: i = 20 A
- Voltage: v = 230 V
- Time: t = 2h = 7200 s

1. q = i * t =20 A * 7200 s = 144,000 C = 144 kC
2. p = v * i = 230 * 20 = 4600 W = 4,6 kW
3. c_tot = c * E = c * p * t = 20 cts/kWh * 4,6 kW * 2h = 184 cents

Question 3

Q: In the figure on the right, you see a schematic drawing of an electric circuit. All the element voltages and currents are specified.

     a. Do they adhere to the passive sign convention? [...]

     b. Find the power absorbed by each element:

          a: [...] W          b: [...] W          c: [...] W

          d: [...] W          e: [...] W

     c. Find the total power absorbed in the circuit: [...] W
A: Yes/yes; -4/-4.0; 10/10.0; 9/9.0; -20/-20.0; 5/5.0; 0

a. The elements adhere to the passive sign convention because for all of them i enters the elements at the (+) terminal

b.

Element    Voltage (V)     Current (A)     Power (W)

a                 -2                  2                  -4

b                  5                  2                  10

c                  3                  3                   9

d                  4                 -5                 -20

e                  1                  5                  5

c. p_total= -4 + 10 + 9 - 20 + 5 = 0

[Image: circuit drawing]