ECEN 1400
Midterm 1
Name:
1. (15 POINTS / 100)
Given the transformer circuit below, a) what is the turns ratio NP / NS and b) what is the
peak current on the primary (left) side?
5 points:VS = IR = (1A ) (1kΩ ) = 1kV peak
VP N P 100
1
=
=
=
VS N S 1000 10
I
N
N
5 points: P = S , I P = I S S = (1A peak ) (10 ) = 10A peak
IS NP
NP
5 points:
2. (15 POINTS / 100)
What is the power dissipated in the resistor, diode (just the diode) and capacitor in each
of these circuits? The LED is RED. You may round the threshold voltage to the nearest
integer volt for simplicity. You may assume the capacitor circuit has been connected for
a very long time.
a
b
c
5 points: a) P = V2 / R (3 points)= 102 / 2000 = 0.05 = 50 mA (2 points)
5 points: b) The LED voltage drop is about 2V (1 point) so the voltage across the resistor
is 8 V (1 point) and thus the current is 8 V / 800 Ohms = 10 mA (1 point). The power
dissipated in the diode is P = V I = (2V)(10 mA) = 20 mW. (2 point)
5 points: c) The current is zero since the capacitor is open (3 points). P = V I = (10V)(0
A) = 0 W (2 points)
Fall 2014
1
ECEN 1400
Midterm 1
Name:
3. (20 POINTS / 100)
In the two circuits below the polarity of the DC voltage source is reversed. Assume the
diode is a typical silicon diode. 1) Given the magnitude of the source voltage relative to
the diode threshold, which diode model should be used here? 2) Using this diode model,
what is the equivalent resistance of each circuit as seen by the source? Hint: Choose the
right diode model, then consider new circuits using this model.
a
b
1: 10 points: The correct diode model, given that 100 V is >> than the typical 0.7V
threshold of a silicon diode, is that the diode is either a short if forward biased or an open
if reverse biased. Half credit (5 points) if choose to include a threshold in the model.
The circuits thus are equivalent to:
2: Thus a) REq = 500 Ohms (5 points) and b) REq = 1KOhm (5 points). If you replaced
the forward-biased diode with a threshold voltage, you can’t really solve for the
resistance, but full credit in this part for the right answer.
4. (15 POINTS / 100)
A 100 Ohm resistor is dissipating an average power of 50 Watts. Assuming the source is
a sinusoidal function, what is the peak-to-peak voltage of across the resistor?
2
5 points: PAverage = VRMS
R∴VRMS = R PAverage
5 points: VPeak = 2VRMS = 2 R PAverage
5 points: VPeak−to−Peak = 2VPeak = 2 2 R PAverage = 2 2 ×100 × 50 = 200 [V ]
Fall 2014
2
ECEN 1400
Midterm 1
Name:
5. (15 POINTS / 100)
You need to accurately measure the current in a simple circuit consisting of a 10V DC
source and a load of unknown resistance that is approximately in the KΩ range.
Unfortunately, your current meter is broken. Your TA suggests putting a resistor in
series (as shown by the resistor labeled R) and using your voltmeter to get the current.
a) Do you place the voltmeter in series with or in parallel with R?
b) Given the voltage across the resistor is measured to be VR, write down a formula for
the current through the 1KOhm resistor.
c) What value would you pick for R and why? Hint: Consider the original goal.
5 points: a) In parallel – a voltmeter in series is
an open.
5 points b) I = VR / R. The current is the same
through both resistors, so we may apply
Ohm’s law to R to find the current through the
load.
5 points c) We want a small resistance so we don’t change the current much from
the original problem. If the resistance was less than 10 Ohms, the answer would
be accurate to 1%.
6. (20 POINTS / 100)
A piece of high voltage equipment contains a capacitor that might be a shock hazard even
after the power is disconnected. Find an equation for the resistance, R, such that the
capacitor will discharge to a safe voltage VSAFE in a time t after the high voltage V0 is
disconnected. VSAFE is less than V0.
Fall 2014
3
ECEN 1400
Midterm 1
Name:
⎡ t ⎤
10 points: VSAFE = V0 exp ⎢ −
⎣ RC ⎥⎦
VSAFE
⎡ t ⎤
= exp ⎢ −
V0
⎣ RC ⎥⎦
−
⎛V
⎞
t
= ln ⎜ SAFE ⎟
RC
⎝ V0 ⎠
10 points: R = −
Fall 2014
t
t
=
⎛V
⎞
⎛ V ⎞
C ln ⎜ SAFE ⎟ C ln ⎜ 0 ⎟
⎝ V0 ⎠
⎝ VSAFE ⎠
4