When adding more than two resistors in parallel, such as three parallel resistor

Question

When adding more than two resistors in parallel, such as three parallel resistors Ra, Rb & Re, the inverse of the equivalent resistance 1/Req is found by adding the inverses of the resistances in each parallel branch, 1 1 Req Ra Rb Rc Find the equivalent resistance of the three parallel resistors shown below. If in figure 2, Vs=10V, Ra-100 and R,-20Q, find the voltage across and current through each resistor. How do the voltage drops across parallel branches compare with one another? How does the current divide between the two parallel branches? (Consult figure 2 caption for hints).

Explanation / Answer

Equivalent resistance = 1/Req = 1/10 + 1/20 + 1/5 ======> Req = 2.86 ohm

Ra = 10

Rb = 20

Rc = 5

Vs = 10 V

Current in circuit = I = Vs/Req = 10/2.86 = 3.5 A

Voltage remains same in parallel resistors and current divides.

Voltage across Ra = Voltage across Rb = Voltage across Rc = 10 V

Current acoss Ra = 10/10 = 1 A

Current acoss Rb = 20/10 = 2 A

Current acoss Rc = 5/10 = 0.5 A

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