Question

Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 5.3Ω and 23.4 W, 41.6Ω and 11.2 W, and 12.7Ω and 10.9 W. (a) What is the greatest voltage that the battery can have without one of the resistors burning up? (b) How much power does the battery deliver to the circuit in (a)?

Answer #1

Power dissipated by a resistor is given as

P = I*I*R

So the first step is to determine what the maximum allowed
current would be for each resistor.

23.4W = I^2*5.3

I^2 = 23.4/5.3 = 4.415

I = square root of (4.415) = 2.10 amps

11.2 = I^2*41.6, I = 0.52 amps

10.9 = I^2*12.7, I = 0.93 amps

Now since all three resistors are in series, the current flowing
through one resistor will be the same for all three resistors. The
lowest maximum current is for the 41.6 ohm resistor at 0.52 amps.
So the voltage must not force more than 0.52 amps otherwise the
41.6 ohm resistor will burn up.

The total resistance of the circuit is the sum of all three
resistors assuming an ideal battery.

So R-total = 5.3+41.6+12.7 = 59.6 ohms.

E = I*R

so the maximum battery voltage is E = .52*59.6 = 30.99 Volts

P=V^2/R=(30.99^2)/59.6=16.11 W

Three resistors are connected in series across a battery. The
value of each resistance and its maximum power rating are as
follows: 5.4Ω and 28.3 W, 33.8Ω and 9.33 W, and 15.1Ω and 12.6 W.
(a) What is the greatest voltage that the battery can have without
one of the resistors burning up? (b) How much power does the
battery deliver to the circuit in (a)?

Three resistors are connected in series across a battery. The
value of each resistance and its maximum power rating are as
follows: 4.2Ω and 22.5 W, 25.6Ω and 13.1 W, and 21.7Ω and 10.4 W.
(a) What is the greatest voltage that the
battery can have without one of the resistors burning up?
(b) How much power does the battery deliver to
the circuit in (a)?

Interactive Solution 20.47 provides one approach to problems
like this one. Three resistors are connected in series across a
battery. The value of each resistance and its maximum power rating
are as follows: 5.0Ω and 24.5 W, 38.3Ω and 12.0 W, and 13.4Ω and
13.9 W. (a) What is the greatest voltage that the
battery can have without one of the resistors burning up?
(b) How much power does the battery deliver to the
circuit in (a)?

Interactive Solution 20.47 provides one approach to problems
like this one. Three resistors are connected in series across a
battery. The value of each resistance and its maximum power rating
are as follows: 6.2Ω and 22.7 W, 33.8Ω and 12.7 W, and 14.7Ω and
10.1 W. (a)What is the greatest voltage that the
battery can have without one of the resistors burning up?
(b) How much power does the battery deliver to the
circuit in (a)?
*** The answers are...

Series/Parallel Circuits: When unequal resistors are connected
in series across an ideal battery,
the same power is dissipated in each one.
the potential difference across each is the same.
the equivalent resistance of the circuit is equal to the
average of all the resistances.
the current flowing in each is the same.
the equivalent resistance of the circuit is less than that of
the smallest resistor.

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battery, which supplies them with a total power of 6.9 W. While the
battery is still connected, one of the resistors is heated so that
its resistance doubles. The resistance of the other resistor
remains unchanged. Find (a) the initial resistance of each
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(a) What is the equivalent resistance of six resistors connected
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_______Ω
(b) Determine the current flowing through each of the six
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_______A
(c) If the six resistors were instead connected in parallel across
the battery, what would be the equivalent resistance?
_________ Ω
(d) Determine the current through each resistor for this parallel
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_________A

A circuit consists of three resistors,
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A)Rank these resistors in order of decreasing current through
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When two unknown resistors are connected in series with a
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_____Ω (lower resistance)

Resistors R1 = 20 W, R2 = 40 W,
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a) Find the equivalent resistance connected across the
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