An electric kettle rated as 2000 W at 220 V is used to warm 2.0 L of water from 15^∘ C to 90^∘ C

step 1 In this question, we are given information about the kettle. Okay, so it's rated at 2 ,000 watts

An electric kettle rated as 2000 W at 220 V is used to warm...

An electric kettle rated as $2000 \mathrm{W}$ at $220 \mathrm{V}$ is used to warm $2.0 \mathrm{L}$ of water from $15^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. (a) How much current flows in the kettle? (b) What is the resistance of the kettle? (c) How long does it take to warm the water? (Specific heat capacity of water $=4200$ $\text { J } \mathrm{kg}^{-1} \mathrm{K}^{-1} \text {.) }$ (d) How much does this cost if the power company charges 0.10 dollar per $\mathrm{kW}$ h?

An electric kettle rated as $2000 \mathrm{W}$ at $220 \mathrm{V}$ is used to warm $2.0 \mathrm{L}$ of water from $15^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$.
(a) How much current flows in the kettle?
(b) What is the resistance of the kettle?
(c) How long does it take to warm the water? (Specific heat capacity of water $=4200$ $\text { J } \mathrm{kg}^{-1} \mathrm{K}^{-1} \text {.) }$
(d) How much does this cost if the power company charges 0.10 dollar per $\mathrm{kW}$ h?

Key Concepts

Time Calculation Using Power

Time calculation using power relates the energy required for a task to the rate at which energy is delivered. Once the total energy (such as heat required for a temperature change) is known, the time required can be found using t = Q/P, where Q is the energy and P is the power. This relationship is important for estimating the duration of energy-dependent processes.

Energy Calculation for Heating

Energy calculation for heating involves determining the amount of thermal energy needed to change the temperature of a substance. This is typically performed using the equation Q = m c ?T, which takes into account the mass of the substance, its specific heat capacity, and the desired temperature change. This concept is central in problems involving heating or cooling processes.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). It is a critical property in thermodynamics that enables one to calculate the energy required to heat or cool a material, using the formula Q = m c ?T, where Q is the thermal energy, m is the mass, c is the specific heat capacity, and ?T is the change in temperature.

Cost Calculation from Energy Consumption

Cost calculation from energy consumption involves converting the energy used by a device into a monetary cost, typically by converting units (such as from joules to kilowatt-hours) and multiplying by the rate charged per unit of energy. This process is important for understanding the economic impact of operating electrical appliances and optimizing energy usage.

Ohm's Law

Ohm's Law is a foundational concept in electronics and electricity that relates the voltage across a conductor to the current flowing through it and its resistance. It is expressed as V = IR, where V is voltage, I is current, and R is resistance. This law allows us to determine any one of these quantities if the other two are known.

Electrical Power

Electrical power is the rate at which electrical energy is consumed or converted into another form of energy. It is defined by the equation P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes. This fundamental relation is used to analyze how devices operate when supplied with electricity.

Resistance Calculation

Resistance is a measure of how much a component or circuit opposes the flow of electric current. Using the formulas from electrical power and Ohm's Law, the resistance of an electrical appliance can be calculated by rearranging the equation relating power, voltage, and resistance, typically as R = V²/P. This helps in understanding and predicting the behavior of electrical devices.

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