Aresistor is connected in series with an ac source that provides a sinusoidal voltage of v of t is equal to v times cosine of begin quantity omega times t end quantity, where v is the maximum voltage, omega is the angular frequency, and t is the time. the current supplied by this source that flows through this resistor is described with the function i of t is equal to i times cosine of begin quantity omega times t end quantity, where i is the maximum current. what is the average power supplied by this ac source?

In circuits, the average power is defined as the average of the instantaneous power  over one period. The instantaneous power can be found as:

So the average power is:

But:

So:

In terms of RMS values:

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.