Question

an electric circuit includes a voltage source and two resistances (50 and 75) in parallel. determine the voltage source required to provide 1.6 A of current through the 75 ohm resistance

Answer 1

Answer:

120 volts

Explanation:

Since the two resistances are connected in parallel across the voltage source, the effective resistance of the circuit can be obtained by using the formula.

$\frac{1}{R_{eq}}=\frac{1}{R_{1}}+ \frac{1}{R_{2}}$

given that $R_{1} and R_{2}$  are 50 and 75 ohms respectively, we have the equivalent resistance as:

$\frac{1}{R_{eq}}=\frac{1}{50}+ \frac{1}{75}=\frac{1}{30}$

hence,

$R_{eq}= 30\Omega$

From Ohm's law, voltage = current X resistance.

given that the current through the 75 ohm resistor is 1.6 A

$V= I\times R$

$V= 1.6 \times 75\Omega$

voltage = 120 Volts.

Because the resistors are connected in parallel, it means that they are connected to the same voltage source.

Hence, the voltage source for the 75 Ohm resistance = 120 volts. This is same for the 50 Ohm resistor.

Answer 2

Answer:

The voltage source required to provide 1.6 A of current through the 75 ohm resistance is 120 V.

Explanation:

Given;

Resistance, R₁ = 50Ω

Resistance, R₂ = 75Ω

Total resistance, R = (R₁R₂)/(R₁ + R₂)

Total resistance, R = (50 x 75)/(125)

Total resistance, R = 30 Ω

According to ohms law, sum of current in a parallel circuit is given as

I = I₁ + I₂

$I = \frac{V}{R_1} + \frac{V}{R_2}$

Voltage across each resistor is the same

$1.6 = \frac{V}{R_2}$  

V = 1.6 x R₂

V = 1.6 x 75

V = 120 V

Therefore, the voltage source required to provide 1.6 A of current through the 75 ohm resistance is 120 V.

This voltage is also the same for 50 ohms resistance but the current will be 2.4 A.