Let's explore the relationship between resistance (R) and current (I) when the voltage (V) is kept constant using Ohm's Law. Ohm's Law is given by:
[tex]\[ V = I \times R \][/tex]
From Ohm’s Law, we can rearrange the formula to express current as:
[tex]\[ I = \frac{V}{R} \][/tex]
Here’s a detailed step-by-step explanation to understand the relationship:
1. Define Initial Conditions:
- Let’s consider a constant voltage [tex]\( V = 10 \)[/tex] volts.
- Let the initial resistance [tex]\( R_1 = 5 \)[/tex] ohms.
2. Calculate Initial Current:
- Using Ohm’s Law:
[tex]\[ I_1 = \frac{V}{R_1} \][/tex]
Substituting the values:
[tex]\[ I_1 = \frac{10}{5} = 2.0 \][/tex] amperes.
3. Double the Resistance:
- Now, we double the initial resistance:
[tex]\[ R_2 = 2 \times R_1 = 2 \times 5 = 10 \][/tex] ohms.
4. Calculate New Current with Doubled Resistance:
- Using Ohm’s Law again for the new resistance:
[tex]\[ I_2 = \frac{V}{R_2} \][/tex]
Substituting the values:
[tex]\[ I_2 = \frac{10}{10} = 1.0 \][/tex] ampere.
So, let's summarize the findings:
- Initially, with a resistance of 5 ohms, the current was 2.0 amperes.
- After doubling the resistance to 10 ohms, the current decreases to 1.0 ampere.
Thus, we can conclude:
- For a constant voltage, resistance is inversely proportional to current. When the resistance doubles, the current is cut in half.
Given the answer choices:
1. "Resistance is inversely proportional to current, so when the resistance doubles, the current is cut in half."
This statement is correct.
