Two resistors R_{1} = (4 pm 0.8) , Omega and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For two resistors connected in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$.Subs

Vedclass · Accepted Answer

$(2 \pm 0.3) \, \Omega$

Vedclass · Answer

(C) For two resistors connected in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$.Substituting the given values,$\frac{1}{R_{eq}} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$,which gives $R_{eq} = 2 \, \Omega$.To find the error $\Delta R_{eq}$,we differentiate the expression $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$:$-\frac{\Delta R_{eq}}{R_{eq}^{2}} = -\frac{\Delta R_{1}}{R_{1}^{2}} - \frac{\Delta R_{2}}{R_{2}^{2}}$.Taking the magnitude of errors,$\frac{\Delta R_{eq}}{R_{eq}^{2}} = \frac{\Delta R_{1}}{R_{1}^{2}} + \frac{\Delta R_{2}}{R_{2}^{2}}$.Substituting the values: $\frac{\Delta R_{eq}}{2^{2}} = \frac{0.8}{4^{2}} + \frac{0.4}{4^{2}}$.$\frac{\Delta R_{eq}}{4} = \frac{0.8 + 0.4}{16} = \frac{1.2}{16}$.$\Delta R_{eq} = 4 	imes \frac{1.2}{16} = \frac{1.2}{4} = 0.3 \, \Omega$.Therefore,the equivalent resistance is $R_{eq} = (2 \pm 0.3) \, \Omega$.

Two resistors $R_{1} = (4 \pm 0.8) \, \Omega$ and $R_{2} = (4 \pm 0.4) \, \Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be

Similar Questions

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

What will be the most suitable combination of three resistors $A = 2 \, \Omega$,$B = 4 \, \Omega$,$C = 6 \, \Omega$ so that $\frac{22}{3} \, \Omega$ is the equivalent resistance of the combination?

When two resistances are connected in parallel,the equivalent resistance is $\frac{6}{5} \, \Omega$. When one of the resistances is removed,the effective resistance is $2 \, \Omega$. The resistance of the wire removed will be ................ $\Omega$.

Two wires of the same material and equal length are joined in parallel combination. If one of them has half the thickness of the other and the thinner wire has a resistance of $8\, \Omega$,the resistance of the combination is equal to

$A$ wire has resistance $12\,\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to ................ $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module