Question

Опір електричного нагрівника становить 11 Ом. До мережі якої напруги потрібно підключити нагрівник, щоб потужність електричного струму в ньому була 4,4 кВт?

Answer 1

P=UI
I=U/R
P=U*U/R=U2/R
PR=U2
U=корень(PR)

U=корень(4400*11)=220В

Answer 2

Calculating the Required Voltage for the Electric Heater

To calculate the voltage required to power the electric heater and achieve a power of 4.4 kW, we can use the formula:

Power (P) = Voltage (V) x Current (I)

Given that the resistance of the electric heater is 11 ohms and the power required is 4.4 kW, we can calculate the current using the formula:

Power (P) = (Current (I))^2 x Resistance (R)

Calculating the Current

Let's calculate the current using the given power and resistance:

4.4 kW = (Current (I))^2 x 11 ohms

To find the current (I), we can rearrange the formula:

(Current (I))^2 = 4.4 kW / 11 ohms

(Current (I))^2 = 4000 W / 11 ohms (1 kW = 1000 W)

(Current (I))^2 = 363.64 A

Current (I) ≈ √363.64 A

Current (I) ≈ 19.07 A

So, the current required for the electric heater to achieve a power of 4.4 kW is approximately 19.07 A.

Calculating the Voltage

Now that we have the current, we can use the formula Power (P) = Voltage (V) x Current (I) to calculate the voltage:

4.4 kW = Voltage (V) x 19.07 A

To find the voltage (V), we can rearrange the formula:

Voltage (V) = 4.4 kW / 19.07 A

Voltage (V) = 4400 W / 19.07 A (1 kW = 1000 W)

Voltage (V) ≈ 230.48 V

So, the electric heater needs to be connected to a power supply of approximately 230.48 volts to achieve a power of 4.4 kW with a resistance of 11 ohms and a current of 19.07 A.