Asolenoidal inductor for a printed circuit board is being redesigned. to save weight, the number of turns is reduced by one-half, with the geometric dimensions kept the same. by how much must the current change if the energy stored in the inductor is to remain the same? (a) it must be four times larger. (b) it must be two times larger. (c) it should be left the same. (d) it should be one-half as large. (e) no change in the current can compensate for the reduction in the number of turns.

Option B is correct.

Explanation:

We define our equation for Inductance, that is,

Where is the permeability of the core material

A= is the cross-sectional Area

N is the number of turns

l= is the lenght of the coil in meters

But we need also a expression for the Energy Stored, that equation is given by,

Where,

L is the inductance and I is the current.

We know that U always is going to be proportional to the number of turns and the current.

Therefore we can conclude that the proportion

Always remains same.

In this way the expresion

Then it mus be two times larger

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.

pe = weightxheight = 2000x1000=2,000,000joules