The resistors of $R_1=100\pm3Ω $ and $R_2=200\pm4Ω $ are connected in parallel.Then express equivalent resistance with percentage error.

I know how tho find percentage error if resistors are connected in series connection.

Can any one help me to find the percentage error if resistors are connected in parallel connection??


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There are two approaches you can take here.

The simple way if just to consider what are the max and min values and calculate the resistance is in each case. This is probably fine for this case but is unsatisfactory for more complicated cases where is not clear what values maximise or minimise the resistance.

The more correct approach is to apply the propagation of uncertainty. In this case (and probably 95% of things you encounter) you need two rules in each case it is square of the uncertainty because you these are properties of the variance, while uncertainty is the standard deviation:

1) addition and subtractions sum linearly. i.e. $u_{A+B}^2 = u_A^2 + u_B^2$. Note this formula is identical for $u_{A-B}$, your uncertainty doesn't get smaller.

2) multiplications and divisions the fractional errors sum. i.e $(\frac{u_{AB}}{AB})^2=(\frac{u_A}{A})^2+(\frac{u_B}{B})^2$

For your case note uncertainty in 1 is zero.

Finally, putting my pedant hat on I feel obliged to point out that you are taking about uncertainty not error. An error is what you have when you measure your $100\Omega$ resistor and find it is actually $102\Omega$.


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