Calculations

Question 1

(3) A transformer is 100% efficient.
It has 200 turns on the primary coil and 3000 turns on the secondary coil.
The input voltage is 55 V.
(i) Show that the output voltage is about 800 V.

Answer 1

substitution: (1)
55 200
V 3000

transposition: (1)
V 3000
 200
evaluation / comment: (1)
 825(V) / which is about 800 (V)

Question 2

(2) Calculate the current in the secondary coil when the current in the primary
coil is 0.50 A.

Answer 2

power input = power output
(1)
• I = 0.033 (A) (1)

Question 3

(3) A homeowner fits a solar panel to her roof.
The cost of the solar panel is £4800.
The solar panel supplies an average of 800 kW h of electrical energy to the
National Grid each year.
The homeowner is paid 40p for each kW h of energy supplied to the National Grid.
Calculate the payback time for the solar panels by selling energy to the National
Grid.

Answer 3

substitution (1)
800 x 0.4 / 800 x 40

evaluation of payment (1)
(£)320 / 32000 (p)

evaluation of payback time (1)
15 (years)

Question 4

(3) A windfarm generates 322 MW of electrical power.
The windfarm is connected to a transmission line at a potential difference
of 132 kV.
Calculate the current from the windfarm

Answer 4

transposition (1)
current = power ÷ voltage
substitution (1)
322 000 000 ÷ 132 000
evaluation (1)
 2440 (A)

Question 5

(2) The windfarm produces 322 MW of power.
The windfarm is to be extended by adding 75 improved turbines.
The extended windfarm will then produce a total of 539 MW.
Calculate the power produced by each improved turbine.

Answer 5

calculation to find additional
power generated e.g.
539 – 322 = 217 (MW) (1)
• 2.9 (MW) (1)

Question 6

(3) The step-down transformer has:
  2400 turns on the primary coil
  200 turns on the secondary coil
  a primary voltage of 230 V.
 Calculate the voltage output of the secondary coil.

Answer 6

substitution (1)
2400/200 = 230/ Vs
transposition (1)
(Vs =) 230 x 200/2400
Evaluation (1)
(Vs =) 19 (V)