An immersion heater of resistance R converts electrical energy into thermal energy that is transferred to the liquid in which the heater is immersed. If the current in the heater is I, the thermal energy transferred to the liquid in time t is ?
The answer is I^2RT, but I don't understand why. Please help. Thank You.
power= I^2 R watts.
Energy= power*time
To understand why the thermal energy transferred to the liquid in time t is given by I^2RT, we need to break down the formula and explain each component:
1. I: This represents the current flowing through the immersion heater. Current is a measure of the rate at which charges (electrons) flow through a circuit. The unit of current is Amperes (A).
2. R: This represents the resistance of the immersion heater. Resistance is a measure of how much a component impedes the flow of current. The unit of resistance is Ohms (Ω).
3. T: This represents the time for which the current flows through the immersion heater. The unit of time is usually measured in seconds (s).
Now, let's understand how the formula I^2RT relates to the thermal energy transferred:
According to Ohm's Law, the voltage (V) across a resistor is equal to the product of the current (I) flowing through it and its resistance (R). Mathematically, this can be written as:
V = I * R
The power dissipated (P) in a resistor is given by the product of the voltage across it and the current passing through it. Mathematically, this can be written as:
P = V * I
Substituting the equation V = I * R into the power equation, we get:
P = (I * R) * I
P = I^2 * R
Power is the rate at which energy is transferred or converted. Therefore, the thermal energy (E) transferred to the liquid can be calculated by multiplying the power by time:
E = P * T
E = (I^2 * R) * T
Hence, the formula I^2RT represents the thermal energy transferred to the liquid in time t.
In summary, the formula I^2RT is derived from applying Ohm's Law and the power equation to calculate the thermal energy transferred to the liquid.
To understand why the thermal energy transferred to the liquid in time t is given by I^2RT, you need to understand the concepts of electrical power and the relationship between power, current, resistance, and time.
The electrical power (P) of a device is the rate at which it converts electrical energy into another form, such as thermal energy. It is given by the equation:
P = VI
where V is the voltage across the device and I is the current flowing through it.
In the case of an immersion heater, the voltage is typically constant, so we can rewrite the power equation as:
P = IV
Now, let's consider that the heater is operating for a time period t. The thermal energy transferred to the liquid depends on the amount of electrical energy converted into thermal energy during this time. We can calculate the total electrical energy (E) using the equation:
E = Pt
where P is the electrical power and t is the time.
Substituting the expression for power, we get:
E = (IV)t
Now, we know that the electrical power can be expressed as the product of current and voltage (P = IV). Therefore, we can rewrite the equation as:
E = (I^2V)t
However, we also know that voltage (V) can be written as the product of current (I) and resistance (R) based on Ohm's law (V = IR). Substituting this into the equation, we get:
E = I^2(Rt)
Since we are interested in the thermal energy transferred to the liquid, we can assume that all the electrical energy is converted into thermal energy by the immersion heater. Therefore, the thermal energy transferred to the liquid in time t is equal to the electrical energy, which can be written as I^2RT.
So, the answer to the question is I^2RT, which represents the thermal energy transferred to the liquid by the immersion heater.