in NCERT physics (class XI) a formula is given for calculation of error in equivalent resistance of two resistances when they are connected in parallel
for eg if two resistances are A and B such that:
RA = R1 + ΔR1
RB = R2 + ΔR2
then formula is given:
ΔRp(RP)2 = ΔR1(R1)2 + ΔR2(R2)2
(where Rp =equivalent resistance of 'A' and 'B' in parallel =R1R2R1+ R2)
can somebody please derive this formula ....how this formula came????
23\frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}
differentiate wrt some variable say x
\frac{-1}{R_{p}^{2}}\frac{dR_{p}}{dx}=\frac{-1}{R_{1}^{2}}\frac{dR_{1}}{dx}+\frac{-1}{R_{2}^{2}}\frac{dR_{2}}{dx}
i.e
\frac{\Delta R_{p}}{R_{p}^{2}}=\frac{\Delta R_{1}}{R_{1}^{2}}+\frac{\Delta R_{2}}{R_{2}^{2}}
1huh???
qwerty the ΔR you have proved is different..... it is a purely theortical thing
whereas error ΔR is an experimental quantity...
maybe i m wrong but im not able to satisfy with this
23then tell me the application of that theoritical thing.......
it simply says that if change in Rp is something then the expected chnge in some other quantity will be this much .
1ok
take example of
R = AB
for this, according to your way
\frac{\bigtriangleup R}{R} = \frac{\frac{\bigtriangleup A}{A} - \frac{\bigtriangleup B}{B} }{B^{2}}
but the actual formula for division is:
\frac{\bigtriangleup R}{R} = {\frac{\bigtriangleup A}{A} + \frac{\bigtriangleup B}{B} }
1@pritish
what qwerty has done is correct. He has just maximized the the infinitesmal objects we talk about in differentiation. I believe u're still in 11th thats why u got doubts in it it will be clear nxt year to u.
1ok i agree with you but by this way can you derive the error formula for
division???
plz see the last thing i posted
23@ pritishmast
R = A/B
\frac{dR}{dx}=\frac{B\frac{dA}{dx}-A\frac{dB}{dx}}{B^{2}}
dx gets cancelled frm both sides
dR=\frac{dA}{B}-\frac{AdB}{B^{2}}
divide by R and approximate dR to delta R
\frac{\Delta R}{R}=\frac{\Delta A}{A}-\frac{\Delta B}{B}
buttt, since errors always add up ,
\frac{\Delta R}{R}=\frac{\Delta A}{A}+\frac{\Delta B}{B}
wat this means is if u make an error of delta B in B and delta A in A ,
then the error u get in R will add up due to both
1ohhhhkk
so we can calculate error by this way anywhere......thanx