An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the lengths and radii of the wire are in the ratio `(4)/(3)` and `(2)/(3)`, then the ratio of the currents passing through the wires will be

Options

A. 3
B. `1//3`
C. `8//9`
D. `9//8`

Explanation

To solve the problem of finding the ratio of currents passing through two wires connected in parallel, we will follow these steps:

### Step 1: Understand the relationship between resistance and dimensions
The resistance \( R \) of a wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity (which is constant since both wires are made of the same material), \( L \) is the length of the wire, and \( A \) is the cross-sectional area. The area \( A \) can be expressed in terms of the radius \( r \) as:
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