One lightbulb is marked ·25 W 120 V ' and another 100 W 120 V; this means that each bulb has its

One lightbulb is marked ·25 W 120 V ' and another 100 W 120...

One lightbulb is marked $\cdot 25 \mathrm{W} 120 \mathrm{V}$ ' and another $100 \mathrm{W}$ $120 \mathrm{V}$; this means that each bulb has its respective power delivered to it when plugged into a constant $120-\mathrm{V}$ potential difference. (a) Find the resistance of each bulb. (b) How long does it take for $1.00 \mathrm{C}$ to pass through the dim bulb? Is the charge different in any way upon its exit from the bulb versus its entry? (c) How long does it take for $1.00 \mathrm{J}$ to pass through the dim bulb? By what mechanisms does this energy enter and exit the bulb? (d) Find how much it costs to run the dim bulb continuously for 30.0 days if the electric company sells its product at $\$ 0.0700$ per kWh. What product does the electric company sell? What is its price for one SI unit of this quantity?

Key Concepts

Ohm's Law and Electrical Resistance

Ohm's Law (V = IR) is fundamental in understanding how electrical resistance relates voltage and current. When a device is rated for a specific voltage and power, its resistance can be determined using the relation P = V²/R. This principle allows us to calculate the resistance by rearranging the formula, providing insight into how the device will behave when connected to a particular voltage source.

Electrical Power and Device Ratings

Electrical power describes the rate at which energy is transferred or converted. Devices are often rated in watts (W) for a given voltage, indicating the power consumed when operated at that voltage. This relationship, expressed as P = V²/R, not only sets the conditions for safe operation but also helps in understanding energy consumption and efficiency during operation.

Electric Current and Charge Flow

Electric current is the flow of electric charge, and it is measured in amperes (A), where one ampere represents one coulomb of charge passing through a given point per second. Understanding this concept allows us to compute the time it takes for a given quantity of charge to pass through an electrical component by using the relation I = Q/t, which is central to analyzing current flow in any circuit.

Energy Transfer in Electrical Systems

Energy in electrical systems is quantified in joules (J) and is related to power through the equation E = P × t, where P represents the rate of energy transfer. This concept links the power consumption of a device to the energy transferred over time. It is also essential in understanding how energy flows through a device, such as a lightbulb, and how it is converted into other forms of energy like light and heat.

Electricity Consumption and Energy Billing

Electricity billing is based on the energy consumed, typically measured in kilowatt-hours (kWh). A kilowatt-hour represents the energy usage when a device consumes 1000 watts for one hour. This concept is crucial when calculating the operating cost of an electrical device over time, as it involves converting power ratings and operating durations into energy, and then applying an electricity rate to determine the cost.

Transcript

00:01 Dear learners, in path a, we will find the resistance of the first bulb that will be given by r1 is equal to voltage square divided by power.

00:26 There is equal to the voltage is 120 volts square divided by the power.

00:37 The power of the first bulb is 25 watt there is equal to 576 ohm so this is the resistance of the first bulb for the second bulb r2 is equal to again the potential difference is same there is 120 volt square divided by but this bulb is of 100 watt this is equal to 144 ohms.

01:28 So this is the resistance of second bulb.

01:33 Now in part b, charge is equal to one column.

01:43 This is given and time needs to be calculated.

01:53 We will use the relationship.

01:56 T is equal to the product of v and q divided by power there is equal to potential difference is 120 volts multiply by charge is given there is one column divided by and power we need to find the time for the dim bulb and the power of the dim bulb is 25 volt because the lesser the power the dimmer the bulb so 25 watt bulb is dimmer than the handed watt bulb so 25 we will we will put 25 watt here that is equal to 4 .8 seconds so this is part b in part c we need to find the time and energy is given there is equal to one joules we will use the relationship time is equal to energy divided by power that is equal to energy is one joules divided by the power of dim bulb is 25 watts so that is equal to 0 .04 seconds this is part c in part d, we will find total hours in a month.

04:15 There is equal to there are 24 hours in a day, multiply by there are 30 days in a month.

04:26 So total hours are 7 .20 hours.

04:36 Now, we will find total energy.

04:44 Total energy consumed...

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