To determine whether the line will be active when the heater is switched on, we need to calculate the current that will flow through the circuit when the heater is in operation. We can use Ohm's law, which states that current is equal to voltage divided by resistance, or I = V/R.
The resistance of the heater can be calculated using the formula:
R = V^2/P
where V is the voltage and P is the power of the heater.
In this case, the resistance of the heater is:
R = 240^2/2.75 kW = 20.87 Ω
Using Ohm's law, we can now calculate the current that will flow through the circuit when the heater is on:
I = V/R = 240/20.87 = 11.5 A
Since the current required by the heater (11.5 A) is greater than the circuit breaker rating (10 A), the circuit breaker will trip when the heater is switched on, and the line will not be active.