The capital of a sole trader changes as a result of

Capital is what the owner of a sole-trader business has invested in it, and it changes only when transactions directly affect the owner's stake, principally through profits earned, losses incurred, additional capital introduced, or drawings taken out for personal use.

Drawings occur when the owner withdraws cash, goods, or other assets from the business for personal purposes. Paying for something by cheque drawn from the business bank account for the owner's own use reduces what the business owns without the owner supplying anything in return, so it directly reduces the capital account.

The other transactions do not change capital at all: buying equipment by cheque, or buying goods by cheque, simply exchanges one business asset (cash at bank) for another (equipment or stock), leaving total assets, and therefore capital, unchanged. Paying wages by cash is a business expense, which affects net profit for the period and only impacts capital indirectly once that period's profit or loss is eventually transferred to the capital account at year end; it is not the direct, immediate capital movement that drawings represents.

Examination reminder: capital only moves directly when the owner puts something in or takes something out; ordinary asset-for-asset exchanges within the business leave it untouched.