The statement that accurately describes the effect on the accounting equation when the owner contributes cash to the business is: "The cash asset increases with a debit, and owner's equity increases with a credit."
When the owner contributes cash to the business, the cash account is debited (increased) since cash is an asset, and assets are increased with debits. At the same time, the owner's equity account is credited (increased) since the owner has just invested money in the business, and owner's equity accounts are increased with credits. This results in an increase in both the asset and owner's equity accounts, which keeps the accounting equation in balance.