Get personalized answers to your specific questions with IDNLearn.com. Discover comprehensive answers to your questions from our community of knowledgeable experts.

A 0.5 kΩ resistor is connected to a 5-V power supply.

(a) What is the current through the resistor?

(b) How much power is delivered to the resistor?


Sagot :

Alright, let's dive into solving the problem regarding the resistor connected to a power supply.

### Given:
- Resistance, [tex]\( R = 0.5 \)[/tex] kilo-ohms ([tex]\( k\Omega \)[/tex])
- Voltage, [tex]\( V = 5 \)[/tex] volts (V)

### Part (a): What is the current through the resistor?

1. Convert the resistance from kilo-ohms to ohms:
- 1 kilo-ohm is equal to 1000 ohms.
- So, [tex]\( R = 0.5 \)[/tex] kilo-ohms is equal to [tex]\( 0.5 \times 1000 = 500 \)[/tex] ohms.

2. Calculate the current using Ohm's Law:
Ohm's Law states that [tex]\( I = \frac{V}{R} \)[/tex], where [tex]\( I \)[/tex] is the current, [tex]\( V \)[/tex] is the voltage, and [tex]\( R \)[/tex] is the resistance.
- Substituting the given values: [tex]\( I = \frac{5}{500} \)[/tex].
- This gives us [tex]\( I = 0.01 \)[/tex] amperes (A).

So, the current through the resistor is 0.01 A.

### Part (b): How much power is delivered to the resistor?

1. Calculate the power using the formula:
The power delivered to a resistor can be calculated using [tex]\( P = \frac{V^2}{R} \)[/tex], where [tex]\( P \)[/tex] is the power, [tex]\( V \)[/tex] is the voltage, and [tex]\( R \)[/tex] is the resistance.
- Substituting the given values: [tex]\( P = \frac{5^2}{500} \)[/tex].
- This simplifies to [tex]\( P = \frac{25}{500} \)[/tex].
- So, [tex]\( P = 0.05 \)[/tex] watts (W).

Thus, the power delivered to the resistor is 0.05 W.

### Summary:
- The current through the resistor is 0.01 amperes (A).
- The power delivered to the resistor is 0.05 watts (W).
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.