Question

For the circuit shown, calculate

Answer 1

For the circuit shown

a.the total resistance   = R = 35.9 Ω

b. when total current = 2 A, then total voltage  =  V = 71.8 V

c.the current through resistor of resistance 56Ω = I₁ = 1.28 A  

  the current through resistor of resistance 100Ω = I₂ = 0.72 A

Explanation:

a)

Resistors can be connected in series or in parallel. For series combination Resultant resistance of the circuit is given by

R = R₁ + R₂ + R₃ +...........+Rₙ

But is our case as shown in the picture, Both the resistors are connected in parallel and for parallel combination resultant, resultant resistance of the circuit is given by

(1 / R) = (1 / R₁) + (1 / R₂) + (1 / R₃) +.......+ (1 / Rₙ)

So

1 / R = (1 / R₁) + (1 / R₂)

Let

R₁ = 56Ω and R₂ = 100Ω

1 / R = 1/56 + 1/100

1 / R = 39 / 1400

R = 1400 / 39

R = 35.9 Ω

b)

Part b can be solved by Ohm's Law Which is stated as "The current flowing through a circuit is directly proportional to the potential difference across its ends provided the physical state such as temperature of the conductor (circuit) does not change."

Mathematically

V ∝ I

V = IR

Where V is the potential difference across the ends of the conductor and I is the Current flowing through the circuit. R is the resistance of the circuit.

Given data:

Total current = I = 2 A

Resistance = R = 35.9 Ω

Voltage = ?

By Ohm's Law

V = IR

V = 2*35.9

V = 71.8 V

c)

To solve current through each resistor, We can use current division formula which is given as

I₁ = I[ R₂ / (R₁ + R₂) ]

I₂ = I[ R₁ / (R₁ + R₂) ]

Also we can take Voltage across each resistor equal to V = 71.8 V because Potential difference across each resistors connected in parallel remain same . And by using Ohm's law divide the value of potential difference with the value of respective resistor to find the current through each resistors.

By Ohm's Law

V = IR

I = V / R

I₁ = 71.8 / 56

I₁ = 1.28 A

I₂ = V / R

I₂ = 71.8 / 100

I₂ = 0.72 A

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