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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