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In a series circuit each resistor will have the same current passing through it.Â If we assume that the wires connecting the resistors have no resistance, then the total potential difference, V, is given by Kirchhoffâ€™s Voltage Law;
V=V_{1}+V_{2}+V_{3}+â€¦
Using Ohmâ€™s Law,
V=IR,
we get
IR=IR_{1}+IR_{2}+IR_{3}+â€¦
as the current is the same in each resistor we can cancel them out to get;
R=R_{1}+R_{2}+R_{3}+â€¦
Basically if you have 2 or more resistors in **series** the total resistance is simply the **sum** of each resistance.
Combining resistances in parallel is a bit more complicated; in a parallel circuit each resistor will have the same potential difference, but the current flowing through them will not necessarily be the same.Â If we start with the conservation of charge we get;
I=I_{1}+I_{2}+I_{3}+â€¦
using Ohmâ€™s Law again gives us
V/R=V/R_{1}+V/R_{2}+V/R_{3}+â€¦
and as V is the same for all the resistors we get
1/R=1/R_{1}+1/R_{2}+1/R_{3}+â€¦
If you have 2 or more resistors in **parallel **the **reciprocal **of the resistance (1 over the resistance) is the sum of the **reciprocals **of each resistance.

Answered by Matt Q.

Studies Physics at Manchester

A nuclear power station uses rods of radioactive material such as U-235Â to produce heat by means of nuclear fission. This heat is produced in a controlled chain reaction where a neutron is fired at a uranium atom, which splits to produce 2 smaller "daughter" atoms and two or three extra neutrons, as well as some energy. These extra neutrons can go on to split more uranium atoms and repeat the proccess, releasing more energy. This energy is used to boil water to produce steam, which is used to turn turbines attached to generators which produce electricity.
A coal power station differs only in how it produces the energy to boil the water. This energy comes from burning coal, otherwise the electricity is produced in the same manner.

Answered by Lorne F.

Studies Physics at Exeter

This is a proton decaying into a neutron and two other subatomic particles. Here you have to consider various conservation laws, including: baryon number, lepton number and charge. (Energy and momentum are assumed to be conserved.)Â Firstly, baryon number. This is conserved because the baryon number of on the left hand side is 1 (from the proton) and 1 on the right hand side from the neutron.Â Secondly charge must be conserved, This is because on the left hand side there is a proton of charge +1 and on the right hand side there is a neutron of charge 0 so there must be another particle on the right hand side to balance the charge. This is a positron, the antiparticle of the electron (e^{+}). Thirdly, lepton number. On the left hand side of the equation it is zero and on the right hand side of the equation it must therefore also be zero. However, we now have a positron on the right hand side meaning the lepton number on the right hand side is -1 (minus because it's an antiparticle). Therefore another particle with a lepton number of +1, charge 0 and baryon number 0 must be added so that all conservation laws are satisfied. This is a neutrinoÂ Î½.Â Therefore the equation isÂ **p**^{+}Â ----> n + e^{+}Â +Â Î½

Answered by Ryan S.

Studies Physics at Bath

A) 75 rad/s Â Â Â B) 150 rad/s Â Â Â C) 270 rad/s Â Â Â D) 540 rad/s Â Â Â Identify equation as w=v/r Â Â Â Diameter = 0.4m Â Radius Â = half the diameter = 0.2m Â Â Â Velocity needs to be in m/s so 108km/h = 108000m/h = 30m/s (divide by 60 twice). Â Â Â Angular velocity = v/r = 30/0.2 = 150 therefore B is the answer.

Answered by Edward W.

Studies Politics, Philosophy and Economics at Oxford, Lincoln College

The equation is shown below as found in the IB Physcis Data Booklet.
GPE = -G*M*m / r
Where GPE is gravitational potential energy, G is the gravitational constant, M and m are theÂ masses of the objects, and r is the distance between their centres of mass.
This equation is a simplified version of the integral from inifinitityÂ to r of the equation for the force between two point masses,Â which is also in the data booklet. You don't need to know how to do this integration, but you should know the definition for gravitational potential energy which comes from that equation; "the energy required to bring a point mass from an infinitite distanceÂ from M to a distance r from M". Notice that because masses attract each other, this means the masses will move towards each other voluntarily, implying that no energy needs to be put into the system. Therefore, the energy calculated from the equation is negative because the masses would still move towards each otherÂ voluntarily if energy was taken out of the system.
It is true that energy cannot be negative, but really you are using this equation to calculate the difference in potential energy between a point at distance r from M and a point at infinite distance from M. Usually you will need to use this to find the difference in potential energies at different orbits or values of r, which will be positive.

Answered by William L.

Studies General Engineering at Durham

We know that the number of undecayed nuclei, N, is given by N=N_{0}e^{-lambda t}. From this, by setting N=N_{0}/2 we know at this point that t= T_{0.5}Â (the half life) and can show that lambda =ln(2)/T_{0.5}Â . Hence we can calculate lambda as 1.54 x10^{-4}Â days^{-1}. Now using the original form by setting N=0.1N_{0}Â we can get t = -ln(0.1)/lambda=14952 days.

Answered by Luke C.

Studies Mechanical Engineering at Bristol

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