Question

in the circuit given below the resistance R1, R2, R3 (ARE In PARALLEL) have the value of 10 ohm,20ohm, 30 ohm resp, which have been connected to battery of 12 v calculate A) the current through each resistor B)The total resistance C)The total current in the cKt
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Answer 1

Answer:

V=12V

R1, R2 and R3 are connected in parallel.

(a) Current through R1 = V/R1 = 12/5 = 2.4 A

Current through R2 = V/R2 = 12/10 = 1.2 A

Current through R3 = V/R2 = 12/30 = 0.4 A

(b) Total current in the circuit = 2.4 + 1.2 + 0.4 = 4 A

(c) Total resistance in the circuit=R

1/R = 1/R1+ 1/R2 + 1/R

1/R = 1/5 + 1/10 + 1/30

1/R = 10/30

R = 3 ohm

Explanation:

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Answer 2

Given that, R1 = 10 ohm, R2 = 20 ohm, R3 = 30 ohm and V is 12V.

For parallel combination:

1/Rp = 1/R1 + 1/R2 + 1/R3

------------| R1 = 10ohm |-------------

------------| R2 = 20ohm |-------------

------------| R3 = 30ohm |-------------

Substitute the known values,

1/Rp = 1/10 + 1/20 + 1/30

1/Rp = 1/10(1/1 + 1/2 + 1/3)

1/Rp = 1/10(11/6)

Rp = 60/11

Rp = 5.45 ohm

We have to find a) the current through each resistor b) The total resistance c)The total current in the circuit.

a) Ohm's law: The potential difference i.e. V across the ends of the wire is directly

proportional to the current i.e. I flowing

through that wire provides the temperature

remains constant.

From ohm's law we can say that: V = IR

For first resistor:

I1 = V/R1

I1 = 12/10

I1 = 1.2A

For second resistor:

I2 = V/R2

I2 = 12/20

I2 = 0.6A

For third resistor:

I3 = V/R3

I3 = 12/30

I3 = 0.4A

Therefore, the current through the each circuit is 1.2A, 0.6A and 0.4A.

b) The total resistance of the circuit is 5.45 ohm.

c) Total current in the circuit = I1 + I2 + I3

= (1.2 + 0.6 + 0.4)A

= 2.2A