Problem 9 - Applied Physics

Question

Will a 20.0-A fuse blow if a \(1000-\mathrm{W}\) hair dryer, a \(1200-\mathrm{W}\) electric skillet, and an \(11 \overline{0} 0-\mathrm{W}\) toaster are all used at once on a \(11 \overline{0}-\mathrm{V}\) line?

Step-by-Step Solution

Answer

Yes, the fuse will blow because the total current (30 A) exceeds the fuse rating (20 A).

Step 1: Calculate Total Power Consumption

First, add up the power consumption of all the appliances being used. This includes the hair dryer, electric skillet, and toaster. The hair dryer uses 1000 W, the electric skillet uses 1200 W, and the toaster uses 1100 W. So, the total power is:\[ P_{\text{total}} = 1000 \text{ W} + 1200 \text{ W} + 1100 \text{ W} = 3300 \text{ W} \]

Step 2: Calculate Total Current Drawn

Use the formula relating power, current, and voltage: \[ P = IV \]where \(P\) is power, \(I\) is current, and \(V\) is voltage. Rearrange to solve for current:\[ I = \frac{P}{V} \]Substitute the total power and the voltage of the line:\[ I = \frac{3300 \text{ W}}{110 \text{ V}} \approx 30 \text{ A} \]

Step 3: Compare with Fuse Limit

The calculated current (30 A) is greater than the rating of the fuse (20 A). So, a 20.0-A fuse will blow if these three appliances are used simultaneously on a 110-V line.

Key Concepts

Power Consumption

Power consumption tells us how much electrical power an appliance uses to function. It is measured in watts (W). Every electrical device requires a certain amount of power to operate.
For example, in our exercise, we have three appliances: a hair dryer, an electric skillet, and a toaster. Each one has a power rating that adds up to make the total power consumption.

• Hair Dryer: 1000 W
• Electric Skillet: 1200 W
• Toaster: 1100 W

The total power consumption, when all these appliances are used together, is the sum of their individual powers: \(1000 + 1200 + 1100 = 3300\) W.
This is crucial for determining the electrical load on a circuit.

Electrical Appliances

Electrical appliances are devices that require electricity to perform tasks. These can vary widely in the power they require.
Some appliances, like our toaster and hair dryer, are high-power devices meaning they need a significant amount of electricity to work properly. Understanding the power needs of each appliance helps us to safely manage our household electrical usage.
Each device usually has its power consumption listed on a label. This helps us ensure that we don't overload circuits in our homes.

Fuse Rating

A fuse is a safety device used to protect electrical circuits. It helps prevent excessive current which can cause overheating and potentially start fires.
The fuse rating is the maximum amount of current that the circuit can handle before the fuse blows, breaking the circuit to prevent damage. In the example, the fuse is rated at 20 A, meaning it can safely allow up to 20 amperes of current through.
If this limit is exceeded, the fuse will blow. When we calculated the total current drawn by the appliances, it was about 30 A, which is higher than the fuse rating.
Thus, using all these appliances would cause the fuse to blow, which underscores the fuse's role in circuit protection.

Voltage

Voltage is the potential difference that drives current (or flow of electrons) through a circuit. It is measured in volts (V).
In this exercise, the voltage of the power line is given as 110 V, which is common for household circuits.Voltage, along with current, determines how much power an appliance can consume. Using the formula \( P = IV \), where

• \(P\) is the power in watts
• \(I\) is the current in amperes
• \(V\) is the voltage in volts

We can rearrange it to find the current: \( I = \frac{P}{V} \).
This calculation is crucial for understanding whether the appliances will operate within the safe limits of the circuit.