Determine the external resistor required to reduce the line voltage from 120 V to 72 V for the operation of a device. The device is rated for 120 V, 100 W.

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  1. 48 Ω
  2. 96 Ω
  3. 240 Ω
  4. 144 Ω

Answer (Detailed Solution Below)

Option 2 : 96 Ω
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Detailed Solution

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Concept:

Active power drawn by a device, 

P = V2 / Rd

So, Rd = V2 / P        ...(1)

Where,

R= resistance of the device

V = Voltage rating of the device

F1 Harish Batula 13.5.21 Pallavi D17

Explanation:

Given, device rating is 120 V, 100 W

So, from (1), resistance of device 

Rd = (120)2 / 100 = 144 Ω 

Now let's add external resistor Rex in series with device resistance Rd.

F1 Harish Batula 13.5.21 Pallavi D18

Line voltage of device reduces from 120 to 72 V, so the remaining voltage(120 - 72 = 48 V) should drop across Rex.

Current through circuit, 

\(\large{I= \frac{72}{144}=\frac{48}{R_{ex}}}\)

Rex = 96 Ω 

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