Introduction:
A T flip-flop, also known as a toggle flip-flop, is a type of digital circuit that is commonly used in various applications. It has a single input called the "T" input and two outputs, namely the "Q" output and the "Q̅" (Q-bar) output. The T flip-flop can be implemented using various logic gates like NAND gates, NOR gates, or even using other flip-flops.

Explanation:
The correct answer to the given question is option C - "A digital counter and frequency divider." Let's understand why.

Digital Counter:
A T flip-flop can be used as a building block for constructing digital counters. By connecting multiple T flip-flops in a cascaded manner, we can create different types of counters such as binary counters, decade counters, or BCD counters. The T input of each flip-flop in the counter is connected to the output of the previous flip-flop, creating a chain of toggle actions. This allows the counter to increment or decrement its state based on the clock input. Therefore, a T flip-flop is commonly used as a digital counter.

Frequency Divider:
A T flip-flop can also be used as a frequency divider. By connecting the output of a T flip-flop to its T input, we can create a circuit that divides the frequency of the input signal by 2. This is because the T flip-flop toggles its output state whenever a rising or falling edge is detected on its clock input. When the T input is connected to the output, the flip-flop toggles its state on every clock pulse, effectively dividing the frequency by 2. This property of the T flip-flop makes it useful for frequency division applications.

Other Uses:
Although not mentioned in the options, it is worth noting that a T flip-flop can also be used as a delay switch. By connecting the T input to a control signal and the clock input to a clock signal, the output of the flip-flop will change its state after a certain delay determined by the clock frequency. This delay can be used to synchronize signals or control the timing of events in digital systems.

Conclusion:
In conclusion, a T flip-flop is commonly used as a digital counter and frequency divider. It can be used in various applications where counting or frequency division is required. Additionally, it can also be used as a delay switch for controlling the timing of events in digital systems.