Homework Help: Construction of a Circuit

1. May 29, 2012

τheory

1. The problem statement, all variables and given/known data
You are given a battery of 220 V and a radio device that requires 1600 W to run. You are also given four resistors: three 3 Ω resistors and one 20 Ω resistor. What circuit configuration will allow the radio device to run without getting fried?

3. The attempt at a solution

Power = (Voltage)2/Resistance
1600 W = (220 V)2/R
R = 30.25 Ω

So this device would require 30.25 Ω to function correctly. However, based on several circuit configurations, this magnitude of resistance isn't obtainable? For example, if I used just a complete series circuit, then the total resistance would be:

R total = R1 + R2 + R3 + R4
R total = 3 + 3 + 3 + 20 = 29 Ω total which isn't exactly 30.25

Incorporating a parallel circuit would cause resistance values to be even less than their original values because parallel circuits require the reciprocal resistance values. So if I had a circuit consisting of all the resistors parallel, then I would get:

1/R total = 1/R1 + 1/R2 + 1/R3 + 1/R4
1/R total = 1/3 + 1/3 + 1/3 + 1/20
1/R total = 0.95 Ω, which is way less

Thus, can someone point me in the right direction?

2. May 29, 2012

cupid.callin

Ummm ... The question doesn't say that radio works at 220V.
Right? :p

3. May 29, 2012

τheory

What do you mean?

4. May 29, 2012

Zubeen

You made certain mistakes regarding the use of the formula
like-

Since the Resistance is to be attached to the circuit , the V=220 V will be wrong as there will be potential drop across the resistor (if attached in series to the radio).
So we must go like this,
Let V1 be the P.D (potential drop) across the resistor combination (R0 ), and V2 be potential drop across the radio.
Then we have that V1 + V2 = 220.
so since its a series combination of net resistance of the combination and the radio, the current through both of them will be the same.
then,
we have
IR0 + 1600/I =220
on solving , you will get a quadratic equation in terms of I.
Further, since I can be real number only so the D of quadratic equation must be >0
that will give =>
R0 < 121/16
so any combination satisfying above inequality will be the result and similarly , you can check for the parallel combination of radio and net resistance.

Zubeen