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Question: A 42 Ω resistor and a 20 Ω resistor are connected in parallel, and the combination is connected across a 240-V dc line.

(a) What is the resistance of the parallel combination?

(b) What is the total current through the parallel combination?

(c) What is the current through each resistor?

Short Answer

Expert verified

(a) The resistance of the parallel combination is 13.55.

(b)The total current through the parallel combination is 17.70 A.

(c) The current through resistor R1 is 5.71 A and the current through resistor R2 is 12.00 A.x`

Step by step solution

01

Equivalent resistance

Given data:

  • R1= 42 Ω
  • R2= 20 Ω
  • V = 240 V

To find the equivalent resistance of R1 and R2:

The two resistors are in parallel and to calculate their combination we will use the equation :

Req=R1R2R1+R2

Substitute values to find Req as:

Req=R1R2R1+R2=42Ω20Ω42Ω+20Ω=13.55Ω

The resistance of the parallel combination is 13.55 Ω.

02

Total Current

The potential difference V' across resistors connected in the parallel is the same for every resistor and equals the potential difference across the combination and we can use the value of the voltage to find the current across the combination by using Ohm's law as:

It=VReq

Substitute values to find It

It=VReq=240V13.55Ω=17.70A

The total current through the parallel combination is 17.70 A.

03

Current through each resistor

The result in Step 2 represents the total current in the resistors where the total current through resistors connected in parallel is the sum of the currents through the individual resistors R1 and R2.

I1=VR1=240V42Ω=5.71A

But as we discussed in part (b) the voltage is the same and V1 = V2 = 240 V. Now use Ohm's law to get the current in each resistor as:

I2=VR2=240V20Ω=12.00A

The current through resistor R1 is 5.71 A and the current through resistor R2 is 12.00 A.

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