Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

MEDIUM

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What is the formula for calculating the current ratio?

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Important Questions on Current Electricity

HARD

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Two cells of emf

E_{1}

and

E_{2}

have their internal resistance

r_{1}

and

r_{2}

respectively. Deduce an expression for the equivalent emf and internal resistance of their parallel combination when connected across an external resistance

R

assume that the two cells are supporting each other.

MEDIUM

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

If a line makes angles

90 °, 135 °, 45 °

with the

x - axis, y - axis and z - axis

respectively, find its direction cosines.

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

If a line has direction ratios

2, - 1, - 2

then determine its direction cosines.

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

If a unit vector

\vec{a}

makes angles

\frac{π}{3}

with

\hat{i}, \frac{π}{4}

with

\hat{j}

and

θ \in (0, π)

with

\hat{k},

then a value of

θ

is:

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

∆ A B C

has vertices at

A \equiv (2, 3, 5), B \equiv (- 1, 3, 2)

and

C \equiv (λ, 5, μ) .

If the median through

A

is equally inclined to the axes, then the values of

λ

and

μ

respectively are

MEDIUM

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

A B C

is a triangle in a plane with vertices

A (2, 3, 5), B (- 1, 3, 2)

and

C (λ, 5, μ)

. If the median through

A

is equally inclined to the coordinate axes, then the value of

(λ^{3} + μ^{3} + 5)

is

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

The coordinates of a point on the line

\frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{1}

at a distance of

\sqrt{56}

units from the point

(1, 2, 0)

are

MEDIUM

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

In case two cells are identical, each of emf $E = 5 V$ and internal resistance $r = 2 Ω$ , calculate the voltage across the external resistance $R = 10 Ω$

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Which of the following devices does not allow d.c. to pass through?

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

If

A

is a matrix of order

3 \times 3

, then number of minors in determinant of

A

are _____.

MEDIUM

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Write the minor and cofactor of element if the first column of the following matrix and hence evaluate the determinant in each case:

$A = [\begin{matrix} - 1 & 4 \\ 2 & 3 \end{matrix}]$

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Find the minor of the elements of second row of determinant

|\begin{matrix} 2 & 3 & 4 \\ 3 & 6 & 5 \\ 1 & 8 & 9 \end{matrix}|

.

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Write Minors and Cofactors of the elements of determinant:

|\begin{matrix} 2 & - 4 \\ 0 & 3 \end{matrix}|

HARD

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant in case of :

$A = [\begin{matrix} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{matrix}]$

HARD

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Which of the following is not correct in a given determinant of

A

, where

A = {[a_{i j}]}_{3 \times 3}

.

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

If the capital letters denotes the cofactors of the corresponding small letters in the determinant

Δ = |\begin{array}{l} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}|

&

Δ' = |\begin{array}{l} A_{1} & B_{1} & C_{1} \\ A_{2} & B_{2} & C_{2} \\ A_{3} & B_{3} & C_{3} \end{array}|

then

Δ Δ'

equals -

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

The cofactors of first column in the determinant

|\begin{matrix} 5 & 20 \\ 3 & - 1 \end{matrix}|

are

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

In the det.

|\begin{array}{l} 7 & 1 & - 2 \\ 8 & 0 & - 1 \\ - 3 & 2 & - 4 \end{array}|

the value of

C_{23}

is-

EASY

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Find the minor of the element

6

in the determinant

Δ = |\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}|

.

MEDIUM

Physics>Electricity and Magnetism>Current Electricity>Cells, EMF, Internal Resistance

Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant in each case:

$A = [\begin{matrix} 5 & 20 \\ 0 & - 1 \end{matrix}]$