Certainly! Let's go through each part of the problem step-by-step.
### 1.1 Ohm's Law
Ohm's Law states that the current running through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. The formula for Ohm's Law is:
[tex]\[ V = I \cdot R \][/tex]
where:
- [tex]\( V \)[/tex] is the voltage (in volts, V),
- [tex]\( I \)[/tex] is the current (in amperes, A),
- [tex]\( R \)[/tex] is the resistance (in ohms, Ω).
### 1.2 Calculations
#### 1.2 a) Calculate the voltage if the current is 5 A and the resistance is 46 Ω.
Given:
- [tex]\( I = 5 \, \text{A} \)[/tex]
- [tex]\( R = 46 \, \text{Ω} \)[/tex]
Using Ohm's Law:
[tex]\[ V = I \cdot R \][/tex]
[tex]\[ V = 5 \, \text{A} \cdot 46 \, \text{Ω} \][/tex]
[tex]\[ V = 230 \, \text{V} \][/tex]
So, the voltage is 230 V.
#### 1.2 b) Calculate the current, if the voltage is 1150 V and the resistance is 2000 Ω.
Given:
- [tex]\( V = 1150 \, \text{V} \)[/tex]
- [tex]\( R = 2000 \, \text{Ω} \)[/tex]
Rearranging Ohm's Law to solve for the current [tex]\( I \)[/tex]:
[tex]\[ I = \frac{V}{R} \][/tex]
[tex]\[ I = \frac{1150 \, \text{V}}{2000 \, \text{Ω}} \][/tex]
[tex]\[ I = 0.575 \, \text{A} \][/tex]
So, the current is 0.575 A.
#### 1.2 c) If the current is 6 A and the voltage is 420 V, calculate the resistance.
Given:
- [tex]\( I = 6 \, \text{A} \)[/tex]
- [tex]\( V = 420 \, \text{V} \)[/tex]
Rearranging Ohm's Law to solve for the resistance [tex]\( R \)[/tex]:
[tex]\[ R = \frac{V}{I} \][/tex]
[tex]\[ R = \frac{420 \, \text{V}}{6 \, \text{A}} \][/tex]
[tex]\[ R = 70 \, \text{Ω} \][/tex]
So, the resistance is 70 Ω.
### Summary
- The voltage if the current is 5 A and the resistance is 46 Ω is 230 V.
- The current if the voltage is 1150 V and the resistance is 2000 Ω is 0.575 A.
- The resistance if the current is 6 A and the voltage is 420 V is 70 Ω.
