Recent content by Hijaz Aslam

Oh yes! That cleared it out. Thanks blue_leaf77.

Homework Statement The anti-derivative of ∫##\frac{sinx}{sin^2x+4cos^2x}## is ##\frac{1}{\sqrt{3}}tan^{-1}((\frac{1}{\sqrt{3}})g(x))+C## then ##g(x)## is equal to : a. ##secx## b. ##tanx## c. ##sinx## d. ##cosx## Homework Equations ##d(cosx)=-sinx dx## The Attempt at a Solution I tried...

Oh yes! Thanks a lot suremac. I've missed out that point. So, I presume there isn't much to do by taking |(r_1e^{i\theta_1}+r_2e^{i\theta_2})^2|=|(r_1e^{i\theta_1})^2+(r_2e^{i\theta_2})^2+2r_1r_2e^{i(\theta_1+\theta_2})| rather than getting confused. Am afraid that I don't understand the...

Now I want to know how that angle ##\theta_1-\theta_2## crept into the equation? Can you elaborate?

Alright, I think I've made a 'grand' mistake by stating: |(r_1e^{i\theta_1}+r_2e^{i\theta_2})^2|= |r_1e^{i\theta_1}|^2+|r_2e^{i\theta_2}|^2+|2r_1r_2e^{i(\theta_1+\theta_2)}|. Of course |(r_1e^{i\theta_1}+r_2e^{i\theta_2})^2|=...

I am bit confused with the Eueler representation of Complex Numbers. For instance, we say that e^{i\pi}=cos(\pi)+isin(\pi)=-1+i0=-1. The derivation of e^{i\theta}=cos(\theta)+isin(\theta) is carried out using the Taylor series. I quite understand how ##e^{i\pi}## turns out to be ##-1## using...

Homework Statement Q. [/B]The bob of a simple pendulum has a mass ##m## and it is executing simple harmonic motion of amplitude ##A## and period ##T##. It collides with a body of mass ##m_o## placed at the equilibrium position which sticks to the bob. The time period of the oscillation of the...

Alright! So according to the first law of thermodynamics (for an adiabatic process) : \Delta E=Q-W=0-W=-p(dV) From Ideal Gas Law: pV=nRT Differentiating both sides we have: p(dV)+V(dp)=nR(dT) Therefore p(dV)=nR(dT)-V(dp) Substituting the above result in the former equation we have: \Delta...

Thanks for your reply sir! So far I understand that: (1) in an 'isochoric' process the heat supplied to the system (containing gas) is stored as the Internal Energy without any amount of work being done. So we define in such process that ##C_v=\frac{Q}{n\Delta T}## (2) in an 'isobaric'...

I've read in my texts that the there are two kinds of Molar Specific Heat Capacities for gases: 1. Molar Specific Heat Capacity at constant Volume ----- ##C_v## 2. Molar Specific Heat Capacity at constant Pressure ---- ##C_p## And in case of Constant temperature there is no point in...

But I would like to know, why do we obtain the answer for a particular case (here, the magnetic field due to a long wire) using Ampere's Law. I mean if we are asked to find the magnetic field due to a short wire how do we do it? (I heard that Ampere's Law is the general rule for finding the...

I find Ampere's Circuital Law sort of fishy. I don't understand what the actual theory proposes. And the loop that should be taken into consideration adds much to the confusion. How should we select the loop? And in the case of a long wire we find the magnetic field around it by applying...

Thanks for your support everyone. Pardon me for the late reply. NascentOxygen - Thanks! That quite explains why the values of the current are same. But I guess its more challenging to assume that without any mathematics (and that would be handy in competitive examinations.) I should try...

Thanks mfb! :D

BvU- Thanks a lot.