SME
Grade 11 Science · Problem type
Electric power and energy
Use this for “A lamp on 120 V draws 0.5 A. What is its power and resistance, and how much energy does it use in 2 hours?”
Diagram
I
=
V
R
=
120
V
240
Ω
=
0.5
A
Power: 60 W
Time: 2 h
Energy used: 432,000 J
This is an example. Type your own values to start a new problem.
P (W)
=
V (V)
×
I (A)
R
Resistance
calculated
t
Time
example
E
Energy used
calculated
Formulas
P
=
V
×
I
60 = 120 × 0.5
P
=
I
2
×
R
60
=
0.5
2
×
240
E
=
P
×
t
432,000 = 60 × 7,200
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
Power is the energy each second: P = VI, in watts (1 W = 1 J/s).
•
With V = IR, the same power is P = I²R.
•
The energy used is the power times the time: E = Pt, in joules when t is in seconds.
Step-by-step
WE KNOW
V = 120 V, I = 0.5 A, t = 2 h
FIND
power (P), resistance (R), energy used (E)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to s).
t = 2 h = 7,200 s (1 h = 3600 s)
Step 2 · Find power (P)
Use P = V × I
The power is the voltage times the current.
P
=
120
×
0.5
P
=
60
W
Step 3 · Find resistance (R)
Use P = I² × R
Divide the power by the current squared.
R
=
P
/(
I
2
)
R
=
60/(
0.5
2
)
R
=
60/0.25
R
=
240
Ω
Step 4 · Find energy used (E)
Use E = P × t
Each
second
uses
P
joules:
multiply
by
the
seconds.
E
=
60
×
7,200
E
=
432,000
J
Check
Put the numbers back in. Both sides should match.
60 = 120 × 0.5 ✓
60
=
0.5
2
×
240
✓
432,000 = 60 × 7,200 ✓
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