Question
Asked Dec 19, 2019
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Four resistors are connected
to a battery as shown
in Figure P18.12. (a) Determine
the potential difference
across each resistor in
terms of ε. (b) Determine
the current in each resistor
in terms of I.

R = 2R
R = R2
%3D
R4 = 3R
R3 = 4R
Figure P18.12
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R = 2R R = R2 %3D R4 = 3R R3 = 4R Figure P18.12

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Expert Answer

Step 1

The given circuit is reduced in the below figure .

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123 R2 = 2R I2=13= /23 14 I4 R1 =R R43 R23 = R4 = R R234 ww R3 = 4R ww ww ww ww

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Step 2
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Since R, and R, are connected in series , their equivalent resistance is given by R3 = R, + R, R,; = 2R + 4R 23 [1] R; = 6R Since R23 and R, are connected in parallel , their equivalent resistance is given by -4 R,R23 R34 %3D R, +R23 (3R)(6R) 234 3R + 6R [2] R234 = 2R The expxression for total current supplied by the battery is R+2R [3] I = 3R

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Step 3

Continuing previ...

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The potential difference across the resistor R, is given by AV = IR, AV = 3R from equation [3]|| AV = [4] 3 The potential difference across the resistor R, is given by AV, = IR234 (2R) [from equation [3]| AV, = 3R 2ɛ Δν 3 [5] Since the potential difference across the resistor R, is AV, and it is equal to the potential difference across the points a and b den oted as V. ab

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