Series and Parallel Combination of Resistors

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

1. Series combination of $A$ and $C$ connected in parallel with $B$.
2. Parallel combination of $A$ and $B$ connected in series with $C$.
3. Parallel combination of $A$ and $C$ connected in series with $B$.
4. Series combination of $B$ and $C$ connected in parallel with $A$.

Q. Four resistances $10\Omega ,5\Omega ,7\Omega$ and $3\Omega$ are connected so that they form the sides of a rectangle AB, BC, CD and DA respectively. Another resistance of $10\Omega$ is connected across the diagonal AC. The equivalent resistance between A and B is

1. $5\Omega$
2. $2\Omega$
3. $7\Omega$
4. $10\Omega$

Q. Two resistances $R_1$ and $R_2$ provide series to parallel equivalents as $\frac{n}{1}$. Then the correct relationship is

1. ${\left(\frac{R_1}{R_2}\right)}^2+{\left(\frac{R_2}{R_1}\right)}^2=n^2$
2. ${\left(\frac{R_1}{R_2}\right)}^{3/2}+{\left(\frac{R_2}{R_1}\right)}^{3/2}=n^{3/2}$
3. $\left(\frac{R_1}{R_2}\right)+\left(\frac{R_2}{R_1}\right)=n$
4. ${\left(\frac{R_1}{R_2}\right)}^{1/2}+{\left(\frac{R_2}{R_1}\right)}^{1/2}=n^{1/2}$

Q. Find the equivalent resistance between points A and B of the following network shown in the given diagram?

1. $6\Omega$
2. $10\Omega$
3. $4\Omega$
4. $8\Omega$

Q. Given three resistors of $2\Omega ,4\Omega and6\Omega$, what will be the minimum equivalent resistance one can obtain through their various arrangements?

1. $\frac{12}{11}\Omega$
2. $\frac{13}{16}\Omega$
3. $\frac{11}{12}\Omega$
4. $1\Omega$

Q. Find the equivalent resistance between points A and B in the circuit shown in the diagram? Every resistor shown here is of $2\Omega$.

1. $2.33\Omega$
2. $3.33\Omega$
3. $1.33\Omega$
4. $4\Omega$

Q. The effective resistance of a number of resistors in parallel is x$\Omega$. When one of the resistorsis burnt, the effective resistance is y$\Omega$. The resistance of the burnt resistor is.

1. $\left(\frac{xy}{x+y}\right)\Omega$
2. $(y-x)\Omega$
3. $\left(\frac{x+y}{xy}\right)\Omega$
4. $\left(\frac{xy}{y-x}\right)\Omega$

Q. A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is $\alpha$, can be given by

1. $\frac{R}{2\pi }(2\pi -\alpha )$
2. $R(2\pi -\alpha )$
3. $\frac{4\pi }{R\alpha }(2\pi -\alpha )$
4. $\frac{R\alpha }{4{\pi }^2}(2\pi -\alpha )$

Q. Three resistances each of $4\Omega$ are connected in the form of an equilateral triangle. The effective resistance between two corners is

1. $12\Omega$
2. $\frac{3}{8}\Omega$
3. $8\Omega$
4. $\frac{8}{3}\Omega$

Q. The potential difference between points A and B of adjoining figure is -

1. 2 V
2. 2/3 V
3. 8/9 V
4. 4/3 V