Electrical Engineering: Basic Laws (5 of 31) Finding R=? (Resistance) in an Element

Summary

This video tutorial explains how to calculate the resistance of electrical components like resistors or lightbulbs. It outlines two methods: one using Ohm's law with given voltage and current, and another using the power equation when power and voltage are known. The video demonstrates calculations for both a 100-watt and a 60-watt lightbulb connected to a 120-volt source, revealing that resistance increases with lower power consumption.

Takeaways

• 💡 Ohm's Law states that resistance (R) is equal to voltage (V) divided by current (I), represented as R = V/I.
• 🔌 Example: If a voltage of 120 volts and a current of 5 amps are given, the resistance is 24 ohms.
• 🔋 In a circuit where both voltage and power are known, resistance can also be calculated using the power equation.
• ⚡ The power equation states that power (P) is equal to the current squared (I^2) multiplied by the resistance (R).
• 🔍 The current can be found using the equation I = P/V when both power and voltage are known.
• 💡 Example: For a 100-watt light bulb connected to a 120-volt source, the current is 0.833 amps.
• 📏 Resistance for the 100-watt light bulb is calculated as 144 ohms using the equation R = P/I².
• 💡 A 60-watt light bulb connected to the same voltage source (120 volts) draws 0.5 amps of current.
• 📏 The resistance for a 60-watt light bulb is higher at 240 ohms, showing that lower wattage light bulbs have higher resistance.
• 🔄 Lower resistance results in higher current, which leads to more power consumption, explaining why higher-wattage bulbs use more power.

Q & A

What is the formula used to find resistance when both current and voltage are given?

The formula used is Ohm's law, which is R = V / I, where R is resistance, V is voltage, and I is current.

How do you calculate the resistance when the current is 5 amps and the voltage is 120 volts?

Using the formula R = V / I, you would calculate the resistance as R = 120V / 5A, which equals 24 ohms.

What is the approach when you are given power and voltage instead of current?

You use the power equation P = I * V, and Ohm's law (I = V / R) to find the current and then use the formula R = P / I² to calculate resistance.

How do you calculate the current if the power is 100 watts and the voltage is 120 volts?

The current I is calculated using the formula I = P / V, so I = 100W / 120V = 0.833 amps.

Once you know the current, how do you calculate the resistance for a 100-watt light bulb?

Using the formula R = P / I², with P = 100 watts and I = 0.833 amps, the resistance is calculated as R = 100 / (0.833²), which equals 144 ohms.

Why does a 60-watt light bulb have a higher resistance than a 100-watt light bulb?

A 60-watt bulb has a higher resistance because it draws less current for the same voltage. Higher resistance leads to lower current, resulting in lower power consumption.

How do you calculate the resistance for a 60-watt light bulb?

First, calculate the current using I = P / V, so I = 60W / 120V = 0.5 amps. Then, using R = P / I², the resistance is R = 60 / (0.5²) = 240 ohms.

What is the relationship between power, current, and resistance in a circuit?

The power consumed in a circuit is related to the current and resistance by the equation P = I² * R. Higher resistance results in lower current and lower power consumption for a given voltage.

How does the resistance of a device affect the current it draws?

A higher resistance results in a lower current, while a lower resistance allows more current to flow through the device for the same voltage.

What is the general method to calculate the resistance of an electrical device using power and voltage?

First, calculate the current using I = P / V. Then, use the formula R = P / I² to find the resistance.