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Sheet 8h - MATHS

Activity 1: Group Work

1.1 State Ohm's Law and write the formula down, showing the relation between [tex]\(V\)[/tex] (voltage) and [tex]\(R\)[/tex] (resistance).

1.2 Calculate the following:

a) Calculate the voltage if the current is [tex]\(5 \, \text{A}\)[/tex] and the resistance is [tex]\(46 \, \Omega\)[/tex].

b) Calculate the current if the voltage is [tex]\(1,150 \, \text{V}\)[/tex] and the resistance is [tex]\(200 \, \Omega\)[/tex].

c) If the current is [tex]\(6 \, \text{A}\)[/tex] and the voltage is [tex]\(420 \, \text{V}\)[/tex], calculate the resistance.

Sagot :

GinnyAnsweridn
Alright, students, let's dive into Ohm's Law and the related calculations step by step.

### 1.1 Ohm's Law:
Ohm's Law is a fundamental principle in the field of electricity which states that the current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.

The relation between Voltage (V), Current (I), and Resistance (R) is given by the formula:
[tex]\[ V = I \times R \][/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 Calculation:

Let's move on to solving the given problems using Ohm's Law.

#### 1.2 a) Calculate the voltage if the current is 5 A and the resistance is 46 Ω.

Using Ohm's Law, the formula to calculate Voltage (V) is:
[tex]\[ V = I \times R \][/tex]

Given:
- Current ([tex]\( I \)[/tex]) = 5 A
- Resistance ([tex]\( R \)[/tex]) = 46 Ω

Substitute the given values into the formula:
[tex]\[ V = 5 \, \text{A} \times 46 \, \text{Ω} \][/tex]

Perform the multiplication:
[tex]\[ V = 230 \, \text{V} \][/tex]

So, the voltage [tex]\( V \)[/tex] is [tex]\( 230 \)[/tex] volts.

#### 1.2 b) Calculate the current if the voltage is 1150 V and the resistance is 200 Ω.

The formula to calculate Current (I) is:
[tex]\[ I = \frac{V}{R} \][/tex]

Given:
- Voltage ([tex]\( V \)[/tex]) = 1150 V
- Resistance ([tex]\( R \)[/tex]) = 200 Ω

Substitute the given values into the formula:
[tex]\[ I = \frac{1150 \, \text{V}}{200 \, \text{Ω}} \][/tex]

Perform the division:
[tex]\[ I = 5.75 \, \text{A} \][/tex]

So, the current [tex]\( I \)[/tex] is [tex]\( 5.75 \)[/tex] amperes.

#### 1.2 c) If the current is 6 A and the voltage is 420 V, calculate the resistance.

Using Ohm's Law, the formula to calculate Resistance (R) is:
[tex]\[ R = \frac{V}{I} \][/tex]

Given:
- Current ([tex]\( I \)[/tex]) = 6 A
- Voltage ([tex]\( V \)[/tex]) = 420 V

Substitute the given values into the formula:
[tex]\[ R = \frac{420 \, \text{V}}{6 \, \text{A}} \][/tex]

Perform the division:
[tex]\[ R = 70 \, \text{Ω} \][/tex]

So, the resistance [tex]\( R \)[/tex] is [tex]\( 70 \)[/tex] ohms.

### Summary:

1. Voltage calculation: [tex]\( V = 230 \)[/tex] V
2. Current calculation: [tex]\( I = 5.75 \)[/tex] A
3. Resistance calculation: [tex]\( R = 70 \)[/tex] Ω

These are the calculations for the given problems based on Ohm's Law.
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