Dr. Abner Mallity has just discovered the 555 timer. He figures it is a cheap way to get a square wave generator. He needs to generate square wave signals that alternate between 5v and 0v, with a 50% duty cycle. Here is the 555 Timer circuit he has read about.

l What is the period of this circuit?Mallity really needs to control the duty cycle, and he especially needs a circuit that will give 50% duty cycle. He is concerned that the circuit above may not be able to give a duty cycle above 50%. He needs three signals, one at 25% duty cycle, one at 50% duty cycle, and one at 75% duty cycle. He needs you to tell him which of these three duty cycles- if any - can be achieved with this circuit.l What is the duty cycle of this circuit?
l Late at night - when all rationality is gone - Mallity
dreams up an alternative circuit. He asks you to
examine it to determine if it can help.

Now, answer these questions.
l Can the additional resistor be used to control
the duty cycle?l If the duty cycle can be controlled, how does
the duty cycle depend upon the resistors
in the circuit?