Kirchhoff's Junction Law

Q. A short electric dipole has a moment of $16\times {10}^{-9}\text{Cm}$. The electric potential due to the dipole at a point at distance of $0.6\text{m}$ from the centre of the dipole, situates on a line making an angle of ${60}^{\circ }$ with the dipole axis is

1. Zero
2. $50\text{V}$
3. $200\text{V}$
4. $400\text{V}$

Q. An ac circuit has an inductor and a resistor of resistance $R$ in series, such that $X_L=3R.$ Now, a capacitor is added in series such that $X_C=2R.$ The ratio of new power factor with the old power factor of the circuit is $\sqrt{5}:x.$ The value of $9x$ is ______.

Q.

In the figure shown, the current in the 10 V battery is close to

1. $0.21A$ from positive to the negative terminal

2. $0.36A$ from negative to the positive terminal

3. $0.42A$ from positive to the negative terminal

4. $0.71A$ from positive to the negative terminal

Q. The primary of a transformer when connected to a dc battery of $10V$ draws a current of $1mA$. The number of turns of the primary and secondary windings are $50$ and $100$ respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively

1. $20V$ and $2.0mA$
2. $10V$ and $0.5mA$
3. Zero volt and therefore no current
4. $20V$ and $0.5mA$

Q.

Two resistors X and Y of resistances $2\text{ohm}$ and $3\text{ohm}$ respectively are first joined in parallel and then in series. In each case, the voltage supplied is $5\text{V}$.

(i) Draw the circuit diagram to show the combination of resistors in the parallel connection.

(ii) Calculate the voltage across the $3\text{ohm}$ resistor in the series combination of resistors.

Q. Determine the current in the following circuit

1. 1 A
2. 2.5 A
3. 0.4 A
4. 3 A

Q. The given four terminal network is part of a larger circuit. The points $A,B,C$ are at the same potential. The potential difference between any one of $A,B$ or $C$ and $D$ is $40\text{V}$. The potential difference between $A$ and $O$ is

1. $10\text{V}$
2. $15\text{V}$
3. $18\text{V}$
4. $20\text{V}$

Q. Three resistance are joined to form a letter $Y$, as shown in figure. If the potentials of the terminals $A,B$ and $C$ are $6\text{V},3\text{V}$ and $2\text{V}$ respectively, then the potential of the point $O$ will be

1. $4\text{V}$
2. $3\text{V}$
3. $2.5\text{V}$
4. $0\text{V}$

Q.

Kirchhoffs first law is based on?

Q. The magnitude of i in ampere unit is

1. None of these
2. 0.1
3. 0.3
4. 0.6

Q. Explain why electric current is not a vector quantity.

Q. The figure shows a network of currents. The magnitude of current is shown here. The current i will be

1. 23 A
2. – 3 A
3. 3 A
4. 13 A

Q. Two batteries with e.m.f $12V$ and $13V$ are connected in parallel across a load resistor of $10\Omega .$ The internal resistance of the two batteries are $1\Omega$ and $2\Omega$ respectively. The voltage across the load lies between

1. $11.4V$ and $11.5V$
2. $11.7V$ and $11.8V$
3. $11.6V$ and $11.7V$
4. $11.5V$ and $11.6V$

Q. Two identical capacitors $A$ and $B$, charged to the same potential of $5\text{V}$ each, are connected in two different circuits, as shown below, at the time instant $t=0$. If the charge on capacitors $A$ and $B$ at time $t=CR$, is $Q_A$ and $Q_B$ respectively, then $\left(\text{Here,}e\text{is the base of natural logarithm.}\right)$

1. $Q_A=\frac{CV}{e},Q_B=\frac{CV}{2}$
2. $Q_A=CV,Q_B=CV$
3. $Q_A=CV,Q_B=\frac{CV}{e}$
4. $Q_A=\frac{CV}{2},Q_B=\frac{CV}{e}$

Q. The $n$ row each containing $m$ cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of $3\Omega$ resistance. If the total number of cells used are $24$ and internal resistance of each cell is $0.5$ $\Omega$, then

1. $m=8,n=3$
2. $m=6,n=4$
3. $m=12,n=2$
4. $m=2,n=12$

Q. The value of $V_0$ in the following diagram is

1. 4V
2. 6V
3. 8V
4. 10V

Q. A part of a complete circuit is shown in the figure. At some instant, the value of current I is $1\text{A}$ and it is decreasing at a rate of ${10}^2{\text{As}}^{-1}$. The value of the potential difference $(V_P-V_Q)$ ( in volts ) at that instant, is

Q. Which of the following equations is a correct equation for the electrical circuit shown in the figure?

1. ${\epsilon }_1-(i_1+i_2)R-i_1{r}_1=0$
2. ${\epsilon }_2-i_2{r}_2-{\epsilon }_1-i_1{r}_1=0$
3. $-{\epsilon }_2-(i_1+i_2)R+i_2{r}_2=0$
4. ${\epsilon }_1-(i_1+i_2)R+i_1{r}_1=0$

Q. A circuit has a section $\text{AB}$ as shown in figure. If $V_A-V_B=20\text{V}$, then the potential difference across capacitors $C_1$ and $C_2$ are respectively

1. $5\text{V}$ and $10\text{V}$
2. $10\text{V}$ and $5\text{V}$
3. $20\text{V}$ and $10\text{V}$
4. $10\text{V}$ and $20\text{V}$

Q. The given infinite grid consists of hexagonal cells of six resistors each of resistance R. Then $R_{12}$ is equal to

1. $\frac{R}{3}$
2. $\frac{2R}{3}$
3. $\frac{4R}{3}$
4. $\frac{3R}{4}$

Q.

How is potential gradient measured?

Q.

There are $10$ lamps in a hall.

Each one of them can be switched on independently.

The number of ways in which the hall can be illuminated is?

1. $102$

2. $1023$

3. $210$

4. $10!$

Q. A short electric dipole has dipole moment of $2.4\times {10}^{–10}\text{C-m}$. The electric potential due to the dipole at a point at a distance of $0.4\text{m}$ from the centre of the dipole situated on a line making an angle ${60}^{\circ }$ with the dipole axis is -

1. $3.25\text{V}$
2. $4.55\text{V}$
3. $6.75\text{V}$
4. $12.50\text{V}$

Q. Each resistance of the circuit shown in diagram is $r$. The equivalent resistance across the points $\text{A}$ and $\text{B}$ is

1. $r$
2. $\frac{r}{4}$
3. $\frac{r}{2}$
4. $\frac{5r}{8}$

Q. Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of $V_0$ volt. If one of the capacitors is completely immersed in a liquid with dielectric $K$, the potential difference between the plates of the other capacitor will change to $\frac{K}{K+n}{V}_0$, then find the value of $n$.

Q. An inductance $L$ and a resistance $R$ are first connected to a battery. After attaining steady state, the battery is disconnected but $L$ and $R$ remain connected in a closed circuit. Then, the current reduces to $37\%$ of its initial value in time -

1. $RL$
2. $\frac{R}{L}$
3. $\frac{L}{R}$
4. $\frac{1}{LR}$

Q. Figure shows a meter bridge wire $AC$ with a uniform cross-section. The length of wire $AC$ is $100\text{cm}$. $X$ is a standard resistor of $4\Omega$ and $Y$ is a coil. When $Y$ is immersed in melting ice the null point is at $40\text{cm}$ from point $A$. When the coil $Y$ is heated to ${100}^{\circ }C$, a $12\Omega$ resistor has to be connected in parallel with $Y$ in order to keep the bridge balanced at the same point. The temperature coefficient of resistance of the coil $Y$ is $x\times {10}^{-2}$. The value of $x$ is

Q. In the circuit shown in figure, cells of emf 2, 1, 3 and $1\text{V}$, respectively and resistances $2\Omega ,1\Omega ,3\Omega$ and $1\Omega$ are their internal resistances respectively. The potential difference between $D$ and $B$ is given as $\frac{n}{13}$ volts. Find $n$.

Q. Three capacitors of capcitances $3\mu \text{F}$, $4\mu \text{F}$ and $6\mu \text{F}$ are charged upto a potential difference of $2V,3V$ and $4V$ respectively. If terminal $\text{a}$ is connected with $\text{f,}$ terminal $\text{e}$ is connected with $\text{d}$ and $\text{c}$ is connected with $\text{b}$ then find the charge flowing through the circuit?

1. $24\mu \text{C}$
2. $12\mu \text{C}$
3. $16\mu \text{C}$
   
4. $9\mu \text{C}$
   

Q. The four charges -q, -2q, -q, and 4q are placed on four verticers A, B, C and D of a square respectively. Calculate the dipole moment of the system