In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 5 A (amperes), the resistance is 30 ohms. What is the resistance when the current is 6 A ?

1 answer

According to the information given, the current \( I \) varies inversely with the resistance \( R \). This relationship can be expressed mathematically as:

\[ I \times R = k \]

where \( k \) is a constant.

From the problem, when \( I = 5 \) A, \( R = 30 \) ohms. We can calculate the constant \( k \):

\[ k = I \times R = 5 , \text{A} \times 30 , \text{ohms} = 150 , \text{A} \cdot \text{ohms} \]

Now, we need to find the resistance \( R \) when the current \( I \) is 6 A. Using the constant \( k \):

\[ k = I \times R \]

Substituting the known values:

\[ 150 = 6 , \text{A} \times R \]

Now, solving for \( R \):

\[ R = \frac{150}{6} = 25 , \text{ohms} \]

Thus, the resistance when the current is 6 A is \( \boxed{25} \) ohms.