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Unformatted text preview: An unknown resistor R is connected to a 13.0 it resistor. and the combination is attached to an
ideal battery. When the two resistors are combined in paralleL the}r consume 3.60 times as much
power as when they are combined in series. Determine the two possible values for R. Solution: When the resistors H and {let’s call it]I H] are combined in series, the total resistance is
R3 = R + R1. “Ellen they are comhined in parallel. the equivalent resistance is given by L_i+i
Its—R Rid The power in each circuit could he written as I2 Rm, hut that’s not especially useful because
we don"t know that. the current in the circuits is the same. {In fact. it’s not!) However. we
do know that the battery is the same For both circuits. So for the series and parallel circuits.
WE} CELII Wl‘ltﬂ DOWOI‘ ﬂﬂllSuIIlﬂﬂl £13 9 52 E 21 1
e_e_ mdﬂ—E—EE+E) Now. we‘re told that the parallel circuit consumes n. = 8.613 times as much power as the
series circuit; this is because the. equivalent resistance in the parallel circuit is lower. This
112103.115 r rigJ :s+a' ﬁre can cancel out the battt'l'jr' emf from both sides of the equation [good thing. since we don"t
know that quantity}. put the left—hand side of the equation over a common denominator,
and rearrange to get R‘i'Rl n e s s
= 2» R R 2H}? 2» R 2— RR R =ﬂ.
RRI R+R1 i + 1] I? 1 +( n} 1 + By the quadratic formula. the two possible answers for R are [it — 1'le :I: {'t’t — BER? — 4R? R:
2 which after a. hit of algebraic simpliﬁcation {ﬁll in the steps!) hecomes u. — 2 :I: u. 11—4
R=r igt JRL According to the given quantities. our two answers are fail] :I: 8.60 4.60
a = '— rﬂfhm m = ...
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 Spring '08
 SEATON

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