MAE140 Linear Circuits Quiz
# 1  January 29, 2002
Answers
Question 1
(a) 1. Power is proportional to
v
2
/R
or
R
∝
v
2
/P
. Thus, if a 100W bulb has resistance
of 60
Ω
, then a 50W bulb should have a resistance of 120
Ω
.
2. If we double the voltage from 110V to 220V, then for the same power we need to
take four times the resistance. So a 100W bulb for Europe would have a resistance of
240
Ω
.
(b) Label the currents and voltages as shown. In this formulation, the power of each
element is given by the product of its applied voltage and its induced current into the
positive voltage terminal.
1.
The current in the resistor is always
i
R
=v
S
/R
because the voltage across it is always
v
R
=v
S
.
Thus the power absorbed by the resistor is
i
R
v
R
=v
S
2
R
regardless of the current
source action.
2.
The voltage across the current source
v
ICS
=
v
S
. The current is
i
ICS
=i
S
.
Thus the power
delivered by the current source is always 
i
S
v
S
. The direction of current and voltage
shown imply that this is always negative, so that the current source always supplies
power.
3.
The current drawn from the voltage source is
i
IVS
=i
R
+i
S
=i
S
v
S
/
R. Thus the power
provided by the voltage source is
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 Fall '04
 Mauricio
 Resistor, Current Source, Voltage drop

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