If a driver gear has larger radius than a driven gear, will a larger gear ratio result in more torque supplied to the driven gear?

Question

Suppose a driver gear has larger radius than a driven gear. For example, we have a pinion with a main disk, where the main disk is larger than the pinion and the pinion is a follower. This is the case in many fishing reels that are "baitcaster" models, such as the following picture diagram,

I am wondering if a larger gear ratio will result in more torque supplied to the driven gear? Specifically, suppose we have two reel models such that the first has a $7$ to $1$ main drive gear to pinion radius, and the second has a $5$ to $1$ ratio. Will the $5$ to $1$ have less torque being supplied to the pinion gear?

Answer 1

Actually it will be the opposite. In any case the smaller the driving gear the higher the torque applied to the driven gear.

Think about the trade off between speed and torque. If you change the gear ratio so your output rpm is higher, then you can assume that you have lost some mechanical advantage as a trade off, ie. your torque is reduced.

Of course any time you make a driving gear larger, that means it will rotate the driven gear more for every rotation of the drive gear, and vice versa when you make it smaller.