Power in Electrical Circuits

Complete Electrical Circuits

What is electrical work?

The transfer of electrical energy by a component.

What symbol is used for work done?

W.

What is the unit of work done?

Joule (J).

What is the relationship between work done and energy transferred?

W = E.

What equation links work done, potential difference and charge?

W = VQ.

What equation links charge, current and time?

Q = It.

Derive the equation for electrical work using voltage, current and time.

Since W = VQ and Q = It, W = VIt.

What equation is used to calculate electrical work done?

W = VIt.

What does V represent in W = VIt?

Potential difference in volts (V).

What does I represent in W = VIt?

Current in amperes (A).

What does t represent in W = VIt?

Time in seconds (s).

What does W represent in W = VIt?

Work done or energy transferred in joules (J).

A bulb has a pd of 7.06 V and a current of 1.45 A for 4.85 s. Calculate the work done.

W = VIt = 7.06 × 1.45 × 4.85 = 49.6 J.

What is electrical power?

The rate of transfer of electrical energy, or the rate of doing electrical work.

What symbol is used for power?

P.

What is the unit of power?

Watt (W).

What does one watt mean?

One joule of energy transferred per second.

What is the general equation for power?

P = E/t.

What equation links power and work done?

P = W/t.

Derive the electrical power equation using W = VIt.

P = W/t = VIt/t = VI.

What is the main equation for electrical power?

P = VI.

What does P = VI tell us?

The power transferred by a component equals the potential difference across it multiplied by the current through it.

A bulb has a pd of 7.06 V and current of 1.45 A. Calculate its power.

P = VI = 7.06 × 1.45 = 10.2 W.

What equations for electrical work and power apply to all components?

W = VIt and P = VI.

What is power dissipation?

The rate at which electrical energy is transferred by a component, often into thermal energy.

What is the basic equation for power dissipated by a resistor?

P = VI.

How can P = I²R be derived?

Substitute V = IR into P = VI: P = I(IR) = I²R.

What equation calculates power when current and resistance are known?

P = I²R.

How can P = V²/R be derived?

Substitute I = V/R into P = VI: P = V(V/R) = V²/R.

What equation calculates power when potential difference and resistance are known?

P = V²/R.

State the three main electrical power equations.

P = VI, P = I²R, and P = V²/R.

When should P = VI be used?

When potential difference and current are known.

When should P = I²R be used?

When current and resistance are known.

When should P = V²/R be used?

When potential difference and resistance are known.

A 470 Ω resistor carries a current of 1.76 A. What equation should be used to find its power?

P = I²R.

A resistor has a pd of 9.0 V and resistance of 470 Ω. What equation should be used to find its power?

P = V²/R.

How does power change with current for a fixed resistance?

Power is proportional to the square of current: P ∝ I².

How does power change with voltage for a fixed resistance?

Power is proportional to the square of voltage: P ∝ V².

What is efficiency?

The ability of a device to transfer energy usefully.

What is the equation for efficiency using energy?

Efficiency = useful energy output ÷ total energy input.

What is the equation for efficiency using power?

Efficiency = useful power output ÷ total power input.

What is the equation for efficiency using work done?

Efficiency = useful work done ÷ total energy input.

What range of values can efficiency have?

Between 0 and 1.

How is efficiency converted into a percentage?

Multiply the decimal efficiency by 100.

Can efficiency be greater than 100%?

No, because useful energy output cannot exceed total energy input.

What happens to energy that is not usefully transferred?

It is dissipated to unwanted energy stores, often as thermal energy or sound.

A bulb has a total power input of 10.2 W and useful light power output of 3.57 W. Calculate its efficiency.

Efficiency = 3.57 ÷ 10.2 = 0.35 = 35%.

Why is efficiency important when comparing electrical devices?

A more efficient device transfers a greater proportion of its input energy usefully and wastes less energy.

An electric heater receives 100 J of electrical energy and transfers 95 J as useful heat. What is its efficiency?

Efficiency = 95 ÷ 100 = 0.95 = 95%.

An electric heater receives 100 J and produces 95 J heat, 4 J sound and 1 J light. How much energy is wasted?

5 J.

Why does efficiency remain the same if a device operates for longer at constant power?

Both useful energy output and total energy input increase in the same proportion with time, so their ratio stays constant.

How can the efficiency of an electric motor be investigated?

Measure the electrical energy supplied to the motor and compare it with the useful gravitational potential energy gained by a lifted mass.

What useful energy transfer occurs when an electric motor lifts a mass?

The mass gains gravitational potential energy.

What equation gives the gravitational potential energy gained by a lifted mass?

ΔEₚ = mgΔh.

What is the electrical energy input to a motor operating for time t?

Einput = VIt.

What equation can be used to calculate the efficiency of a motor lifting a mass?

Efficiency = mgΔh ÷ VIt.

What measurements are needed to determine the efficiency of a motor lifting a mass?

Mass m, height Δh, time t, potential difference V and current I.

How is the potential difference across a motor measured?

Using a voltmeter connected in parallel across the motor.

How is the current through a motor measured?

Using an ammeter connected in series with the motor.

Why should the average pd and current be measured during a motor efficiency experiment?

They may vary while the mass is being lifted, so average values give a better estimate of the electrical energy input.

What is the useful power output of a motor lifting a mass?

Puseful = mgΔh/t.

What is the electrical power input to a motor?

Pinput = VI.

How can motor efficiency be calculated using power?

Efficiency = (mgΔh/t) ÷ VI.

What happens to energy that is not converted into useful gravitational potential energy by a motor?

It is dissipated, mainly as thermal energy and sound.

Why must energy be conserved in an electrical circuit?

Energy cannot be created or destroyed; it can only be transferred between energy stores.

What does it mean when an electrical component does work?

It transfers electrical energy to another energy store.

Give an example of useful energy transfer in a light bulb.

Electrical energy is transferred into light energy.

Give an example of unwanted energy transfer in a light bulb.

Electrical energy is transferred into thermal energy.

Give an example of useful energy transfer in an electric motor.

Electrical energy is transferred into kinetic energy or gravitational potential energy.

What is the relationship between joules and watts?

1 W = 1 J s⁻¹.

What is the relationship between energy, power and time?

E = Pt.

How can electrical energy be calculated if power and time are known?

E = Pt.

How can electrical energy be calculated if voltage, current and time are known?

E = VIt.

State the key work equation for electric circuits.

W = VIt.

State the key electrical power equation.

P = VI.

State the two resistance power equations.

P = I²R and P = V²/R.

State the key efficiency equation.

Efficiency = useful energy output ÷ total energy input.