To find the value of the current in a circuit given the voltage and resistance, we can use Ohm's Law. Ohm's Law states that the current [tex]\( I \)[/tex] flowing through a conductor between two points is directly proportional to the voltage [tex]\( V \)[/tex] across the two points and inversely proportional to the resistance [tex]\( R \)[/tex] between them. The formula is:
[tex]\[ I = \frac{V}{R} \][/tex]
Let's break down the given values:
- Voltage ( [tex]\( V \)[/tex] ) = 10 volts
- Resistance ( [tex]\( R \)[/tex] ) = 1 kiloohm ( [tex]\( 1 \ k\Omega \)[/tex] )
First, we need to convert the resistance from kiloohms to ohms because the standard unit of resistance is ohms ( [tex]\( \Omega \)[/tex] ). Since 1 kiloohm equals 1000 ohms, we have:
[tex]\[ R = 1 \ k\Omega = 1 \times 1000 \ \Omega = 1000 \ \Omega \][/tex]
Now, substituting the given values into Ohm's Law:
[tex]\[ I = \frac{V}{R} = \frac{10 \ \text{V}}{1000 \ \Omega} \][/tex]
[tex]\[ I = \frac{10}{1000} \][/tex]
[tex]\[ I = 0.01 \ \text{A} \][/tex]
Thus, the current [tex]\( I \)[/tex] in the circuit is [tex]\( 0.01 \)[/tex] amperes.
