Current density is the current crossing per unit area. Consider a cylindrical wire of uniform cross-section $A,$ carrying a current $I.$ Imagine a cross-section formed by a " $30^\circ$ -cut" as shown (the wire is not really cut). The current density perpendicular to this cross-section is:

1. $\dfrac{I}{A}$ 2. $\dfrac{I}{A}~\cos30^\circ$

3. $\dfrac{2I}{A}$ 4. $\dfrac{I}{A}~\sin30^\circ$

Subtopic: Current & Current Density |

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Q28:

A thin circular conducting wire is connected at

A, B

$A,B$ where the smaller arc

A B

$AB$ represents

{\frac{1}{4}}^{th}

$\dfrac14^{\text{th}}$ of the circumference. A current flows from

A

$A$ to

B,

$B,$ dividing into two branches

i_{1}

$i_1$ and

i_{2}

$i_2$ at

A .

$A.$ The ratio

i_{1} : i_{2}

$i_1:i_2$ equals:

1.	$3$	2.	$4$
3.	$\dfrac13$	4.	$1$

Subtopic: Combination of Resistors |

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Q29:

Given below are two statements:

Statement I:	Kirchhoff’s current law is a consequence of the conservation of energy as applied to electric circuits.
Statement II:	Kirchhoff’s voltage law is a consequence of the conservation of charge.

1.	Statement I is incorrect and Statement II is correct.
2.	Both Statement I and Statement II are correct.
3.	Both Statement I and Statement II are incorrect.
4.	Statement I is correct and Statement II is incorrect.

Subtopic: Kirchoff's Voltage Law |

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Q30:

The resistance between

A, B

$A,B$ is found to be

500 Ω

$500~\Omega$ while that between

A, C

$A,C$ is

400 Ω .

$400~\Omega.$ The minimum possible value of

R_{2}

$R_2$ is:

1.

100 Ω

$100~\Omega$
2.

200 Ω

$200~\Omega$
3.

400 Ω

$400~\Omega$
4.

900 Ω

$900~\Omega$

Subtopic: Kirchoff's Voltage Law |

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Q31:

Find the equivalent resistance of the circuit between

A, B

$A,B$ shown in the figure when
(a) terminals

C, D

$C,D$ are disconnected (switch

K

$K$ is open)
(b) terminals

C, D

$C,D$ are connected (switch

K

$K$ is closed)

1.

2.5 Ω, 2.5 Ω

$2.5~\Omega,~2.5~\Omega$
2.

2.5 Ω, 2.4 Ω

$2.5~\Omega,~2.4~\Omega$
3.

2.4 Ω, 2.5 Ω

$2.4~\Omega,~2.5~\Omega$
4.

2.4 Ω, 2.4 Ω

$2.4~\Omega,~2.4~\Omega$

Subtopic: Combination of Resistors |

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Q26:

In the Wheatstone Bridge arrangement shown, the resistance

P

$P$ is

2 Ω .

$2~ \Omega.$ The bridge is initially balanced. If P and Q are interchanged: an amount equal to

S

$S$ has to be added to

R

$R$ to restore the balance. The resistance

Q

$Q$ equals (nearly):

1.

2 Ω

$2 ~\Omega$
2.

3.2 Ω

$3.2 ~\Omega$
3.

4 Ω

$4 ~\Omega$
4.

6.4 Ω

$6.4 ~\Omega$

Subtopic: Wheatstone Bridge |

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Q32:

In the circuit shown below

E_{1} = E_{2} = E_{3} = 2 V

$E_1= E_2=E_3= 2~\text{V}$ ,

R_{1} = R_{2} = 4 Ω

$R_1=R_2 = 4~\Omega$ . What is current flowing between points

A

$A$ and

B

$B$ through battery

E_{2}

$E_2$ ?

1.	$2~\text{A}$ from $A$ to $B$
2.	$2~\text{A}$ from $B$ to $A$
3.	$1~\text{A}$ from $A$ to $B$
4.	zero

Subtopic: Kirchoff's Voltage Law |

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Q25:

Two cells having emfs

3

$3$ V and

2

$2$ V are connected in parallel and they give an emf of

0.5

$0.5$ V in the same sense as

3

$3$ V

-

$-$ cell. The internal resistances of the cells are

r_{1}

$r_1$ and

r_{2}

$r_2$ respectively. If one cell is reversed, their combined emf becomes

2.5

$2.5$ V. The ratio of their internal resistances

(\frac{r_{1}}{r_{2}})

$\Big(\dfrac{r_1}{r_2}\Big)$ is:
1.

1

$1$
2.

\frac{1}{2}

$\dfrac12$
3.

\frac{2}{1}

$\dfrac21$
4.

\sqrt{2}

$\sqrt2$

Subtopic: Grouping of Cells |

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Q24:

A

20 V

$20~\text V$ cell delivers the same power to a

2 Ω

$2~\Omega$ resistor as it does to an

8 Ω

$8~\Omega$ resistor. The internal resistance of the cell is:
1.

2 Ω

$2~\Omega$
2.

4 Ω

$4~\Omega$
3.

6 Ω

$6~\Omega$
4.

1.6 Ω

$1.6~\Omega$

Subtopic: Heating Effects of Current |

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Q23:

The current flowing through the left

20 Ω

$20~\Omega$ resistor is:

1.	$1~\text A$	2.	$0.5~\text A$
3.	$2.5~\text A$	4.	$3~\text A$

Subtopic: Kirchoff's Voltage Law |

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1.	$\dfrac{I}{A}$	2.	$\dfrac{I}{A}~\cos30^\circ$
3.	$\dfrac{2I}{A}$	4.	$\dfrac{I}{A}~\sin30^\circ$

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