Question

20.) The current in the circuit shown in figure
is:
3Ω
22
WWW
P
3Ω
WWW
332
w
WW
202
w
w
42
Hole
3 V
(a) 3 A
(c) LA
(b) 2 a
(d) 0.75 A

Answer 1

Answer:

Option d) 0.75 A

The current in the circuit is 0.75 A.

Explanation:

The resistors are :

• R1 = 2 Ω
• R2 = 2 Ω
• R3 = 3 Ω
• R4 = 3 Ω
• R5 = 3 Ω
• R6 = 4 Ω
• R7 = 4 Ω

Battety = 3 V

____________________________

Equivalent resistance of the circuit =

R1 and R2 are parallel,

$\longrightarrow$ 1/RP = 1/R1 + 1/R2

$\longrightarrow$ 1/RP = 1/2 + 1/2

$\longrightarrow$ 1/RP = 2/2

$\longrightarrow$ RP = 1 Ω

Replace R1 and R2 with 1 Ω resistor.

____________________________

R3, R4 and R5 are parallel,

$\longrightarrow$ 1/R3 + 1/R4 + 1/R5

$\longrightarrow$ 1/3 + 1/3 + 1/3

$\longrightarrow$ 3/3

$\longrightarrow$ 1 Ω

Replace R3, R4 and R5 with 1 Ω resistor.

____________________________

R6 and R7 are parallel,

$\longrightarrow$ 1/R6 + 1/R7

$\longrightarrow$ 1/4 + 1/4

$\longrightarrow$ 2/4

$\longrightarrow$ 1/2

$\longrightarrow$ 2 Ω

Replace R6 and R7 with 2 Ω resistor.

____________________________

1 Ω, 1 Ω and 2 Ω resistors are in series,

$\longrightarrow$ RS = 1 + 1 + 2

$\longrightarrow$ RS = 4 Ω

Equivalent resistance of the circuit is 4 Ω.

__________________

Current in the circuit =

• I = ?
• R = 4 Ω
• V = 3 V

$\longrightarrow$ I = V/R

$\longrightarrow$ I = 3/4

$\longrightarrow$ I = 0.75 A

Current in circuit = 0.75 A.

Therefore, the current in the circuit is 0.75 A.

Answer 2

Given :-

Potential difference = 4 V

R1 = 2 Ω

R2 = 2 Ω

R3 = 3 Ω

R4 = 3 Ω

R5 = 3 Ω

R6 = 4 Ω

R7 = 4 Ω

To Find :-

Current

Solution :-

Equivalent resistance for parallel = 1/R1 + 1/R2 + ... 1/Rn

Equivalent resistance for series = R1 + R2 + .. Rn

Since, R1 and R2 in parallel

Equivalent resistance = 1/2 + 1/2

1/Equivalent resistance = 1 + 1/2

1/Equivalent resistance = 2/2

Equivalent resistance = 1 Ω

Also R3, R4 and R5 is in parallel

1/Equivalent resistance = 1/3 + 1/3 + 1/3

1/Equivalent resistance = 1 + 1 + 1/3

1/Equivalent resistance = 3/3

Equivalent resistance = 1 Ω

Now R6 and R7 in parallel

1/Equivalent resistance = 1/4 + 1/4

1/Equivalent resistance = 1 + 1/4

1/Equivalent resistance = 2/4

1/Equivalent resistance = 1/2 Ω

Equivalent resistance = 2  Ω

Now

Total resistance = 1 + 1 + 2

Total resistance = 4 Ω

V = IR

3 = I(4)

3 = 4I

3/4 = I

0.75 = I