MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Mixed Combination of Cells

In Column I, ...

Question

In Column I, the currents through different branches and voltage between different points of the circuit shown are specified as A, B, C and D. In Column II, values are given, one or more of which may correspond to those in Column I.

Open in App

Solution

Let, $I_{1}$ , $I_{2}$ and $I_{3}$ be the currents through the branches of circuit as shown in figure. $V_{a}$ , $V_{b}$ and $V_{c}$ be the potentials at points a, b and c respectively.
For current through different branches we can write,
(i) In loop abca,
$I_{2} + 2 (I_{2} + I_{3}) + I_{1} = 2$
i.e., $I_{1} + 3 I_{2} + 2 I_{3} = 2$ .. (1)
(ii) In loop cadc
$I_{1} + I_{1} - I_{2} + 2 (I_{1} - I_{2} - I_{3}) = 2$
$4 I_{1} - 3 I_{2} - 2 I_{3} = 2$ .. (2)
(iii) In loop debcd
$2 (I_{2} + I_{3}) - 2 (I_{1} - I_{2} -_{3}) + 2 I_{3} = 1$
i.e., $- 2 I_{1} + 4 I_{2} + 6 I_{3} = 1$ ....(3)
Now performing, equation (2) + equation (3) x 2 we get
$5 I_{2} + 10 I_{3} = 4$ ... (4)
and performing, equation (1) x 4 - equation(2) we get
$15 I_{2} + 10 I_{3} = 6$ ....... (5)
$∴ 10 I_{2} = 2$ or $I_{2} = 0.2 A$
And, $10 I_{3} = 4 - 5 x 0.2 = 3$ or $I_{3} = 0.3 A$
Hence, $I_{1} = 2 - 0.6 - 0.6 = 0.8 A$
Now, the potential difference between points a and c is
$V_{a} - 2 + 0.8 = V_{c}$ or $V_{a} - V_{c} = 1.2 V$
and the potential difference between points b and c is
$V_{b} - 2 (0.5) = V c$ or $V_{b} - V_{c} = 1.0 V$
And,
$I_{1} - I_{2} - I_{3} = 0.8 - 0.2 - 0.3 = 0.3 A$

Suggest Corrections

thumbs-up

0

Similar questions

Q. You are given many resistors, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of

50 H z

frequency (the next three circuits) in different ways as shown in Column II. When a current

I

(steady state for DC or rms for AC) flows through the circuit, the corresponding voltages

V_{1}

V_{2}

(indicated in circuits) are related as shown in Column I. Match the two columns.
Column I Column II

i.	$I \neq 0, V_{1}$ is proportional to $I$	a.
ii.	$I \neq 0, V_{2} > V_{1}$	b.
iii.	$V_{1} = 0, V_{2} = V$	c.
iv.	$I \neq 0, V_{2}$ is proportional to $I$	d.
		e.

Q. A series LRC circuit is activated by a sinusoidal ac volage e = E

_{o}

ω

t, with varying frequency

ω

. In Column I, different frequency values are given and in Column II, different responses of the circuit are shown. One or more of items in Column II may match with any of the frequencies given in Column I.

[ω_{o} = \frac{1}{\sqrt{L C}}]

Q. In the circuit shown aside the switch

S

can be moved from

a

b,

connecting either inductance

L

C

R

.when the key is pressed the switch

S

will be at either

a

b

I,

the variation of physical quantities charge,current,voltage etc.in time are given in terms of constants

C^{'} s

K^{'} s

the values of which depends on emf

V, R, L

C

I I,

the physical quantities under different switch positions are given. the variation in column

I

may correspond to one or more quantities of Column

I I

.

Q. You are given many resistors, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50

H z

frequency (the next three circuits) in different ways as shown in Column II. When a current

I

(steady state for DC or rms for AC) flows through the circuit, the corresponding voltages

V_{1}

V_{2}

(indicated in circuits) are related as shown in Column I. Match the two columns. Column I Column II

i	$I \neq 0, V_{1} is proportional to I$	a
ii	$I \neq 0, V_{2} > V_{1}$	b
iii	$V_{1} = 0, V_{2} = V$	c
iv	$I \neq 0, V_{2} is proportional to I$	d
		e

Q. The electrostatic potential due to certain charge distribution is given by V (x, y, z) = -

\frac{V_{o}}{a^{4}}

(x + y + z) xyz. In Column I, the values of electric field (in terms of

\frac{V_{o}}{a}

) and charge density (in terms of

\frac{V_{o} ε_{o}}{a^{2}}

are given. In Column II, different points in space are given. Each value in Column I may correspond to one or more quantities in Column II.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Cell and Cell Combinations

PHYSICS

Watch in App

explore_more_icon

Explore more

Mixed Combination of Cells

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon