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).
