Sure, let's work through these problems step-by-step.
1.1 State Ohm's Law and write the formula down.
Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it. The relationship 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 Calculate the following:
a) Calculate the voltage if the current is 5A and the resistance is 46Ω.
To find the voltage [tex]\( V \)[/tex], we use the formula from Ohm's Law:
[tex]\[ V = I \times R \][/tex]
Here, the current [tex]\( I \)[/tex] is 5 amps (A), and the resistance [tex]\( R \)[/tex] is 46 ohms (Ω).
So,
[tex]\[ V = 5 \, A \times 46 \, \Omega \][/tex]
[tex]\[ V = 230 \, V \][/tex]
Thus, the voltage [tex]\( V \)[/tex] is 230 volts.
b) Calculate the current, if the voltage is 1.150V and the resistance is 2000Ω.
To find the current [tex]\( I \)[/tex], we rearrange the Ohm's Law formula to solve for [tex]\( I \)[/tex]:
[tex]\[ I = \frac{V}{R} \][/tex]
Here, the voltage [tex]\( V \)[/tex] is 1.150 volts (V), and the resistance [tex]\( R \)[/tex] is 2000 ohms (Ω).
So,
[tex]\[ I = \frac{1.150 \, V}{2000 \, \Omega} \][/tex]
[tex]\[ I = 0.000575 \, A \][/tex]
Thus, the current [tex]\( I \)[/tex] is 0.000575 amperes (or 575 microamperes).
c) If the current is 6A and the voltage is 420V, calculate the resistance.
To find the resistance [tex]\( R \)[/tex], we rearrange the Ohm's Law formula to solve for [tex]\( R \)[/tex]:
[tex]\[ R = \frac{V}{I} \][/tex]
Here, the voltage [tex]\( V \)[/tex] is 420 volts (V), and the current [tex]\( I \)[/tex] is 6 amps (A).
So,
[tex]\[ R = \frac{420 \, V}{6 \, A} \][/tex]
[tex]\[ R = 70 \, \Omega \][/tex]
Thus, the resistance [tex]\( R \)[/tex] is 70 ohms.
In summary:
1. The voltage with a current of 5A and a resistance of 46Ω is [tex]\( 230 \, V \)[/tex].
2. The current with a voltage of 1.150V and a resistance of 2000Ω is [tex]\( 0.000575 \, A \)[/tex].
3. The resistance with a current of 6A and a voltage of 420V is [tex]\( 70 \, \Omega \)[/tex].
