DC and AC Meters - Delta Univ
MULTI-RANGE VOLTMETER A multi-range voltmeter consists of a deflection instrument, several multiplier resistors and a rotary switch 21 Multi-range Voltmeter only one of the three multiplier resistors is connected in series with the meter at any time The range of this meter is V Im(Rm R) Where the multiplier resistance, R can be R 1 or R 2 or
Voltage Divider Capacitor RC circuits
Example: impedance of a Voltmeter 11 We want to measure the internal impedance of a voltmeter Suppose that we are measuring V out of the voltage divider: • R TH: 2 100k in parallel, 100k/2 = 50k • V • Measure voltage across R in (V out)= 8V, thus 2V drop across R TH
Measurement of High Voltage Principles Direct measurement of
same conditions 5 times Record the readings from the primary voltmeter and secondary voltmeter Do this experiment for d = 2 0; 2 5; 3; 3 5 If 0 95???? ª1 05 then ????=???? If 0 95???? ???? 1 05???? then ????=f(????) This means that f(????) should be used instead of ???? in above equation ????= ???? k ∗????????
Chapter 21: RLC Circuits
PHY2054: Chapter 21 2 Voltage and Current in RLC Circuits ÎAC emf source: “driving frequency” f ÎIf circuit contains only R + emf source, current is simple ÎIf L and/or C present, current is notin phase with emf
Thevenin equivalent circuits - Iowa State University
1 Use a voltmeter to measure the open-circuit voltage at the port of the circuit: v oc = V Th 2 Connect a short circuit across the output and use an ammeter to measure the short-circuit current: i sc = I N 3 Calculate R Th = V Th / I N To measure V Th and R Th Note that shorting the output may not always be practical For
RC Circuits - Michigan State University
Feb 05, 2014 · 4 RC Circuits VC = V 0 1e 1 ⇡ 0 63V 0 (4 4) VR = V 0 e 1 ⇡ 0 37V 0 (4 5) This means that after t = ⌧ seconds, the capacitor has been charged to 63 of its final value and the voltage across the resistor has dropped to
Lycée qualifiant: - AlloSchool
Exercice 3: : (représentation de la tension – utilisation de voltmètre) On considère le circuit ci-contre 1) Déterminer le sens du courant électrique dans le circuit
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PHY2054: Chapter 21
1Chapter 21: RLC Circuits
PHY2054: Chapter 21
2Voltage and Current in RLC Circuits
AC emf source: "driving frequency" f
If circuit contains only R + emf source, current is simpleIf L and/or C present, current is
not in phase with emfZ, shown later
sin mmm iI t I Z sin m t 2f sin current amplitude mmm iI tI R RPHY2054: Chapter 21
3AC Source and Resistor Only
Driving voltage is
Relation of current and voltage
Current is
in phase with voltage (= 0) i R sin mmm iI tI R sin m t /iRPHY2054: Chapter 21
4AC Source and Capacitor Only
Voltage is
Differentiate to find current
Rewrite using phase (check this!)
Relation of current and voltage
"Capacitive reactance":Current "leads" voltage by 90
sin m qC t i C /cos C idqdt CV t sin Cm qvtC sin 90 C iCV t sin 90 mmm C iI t IX 1/ C XC 1/ C X CPHY2054: Chapter 21
5AC Source and Inductor Only
Voltage is
Integrate di/dt to find current:
Rewrite using phase (check this!)
Relation of current and voltage
"Inductive reactance":Current "lags" voltage by 90
//sin m di dt L t i L /cos m iLt /sin Lm v Ldi dt t /sin 90 m iLt sin 90 mmm L iI t IX L XL L XLPHY2054: Chapter 21
6General Solution for RLC Circuit
We assume steady state solution of form I m is current amplitude is phase by which current "lags" the driving EMFMust determine I
m andPlug in solution: differentiate & integrate sin(
t- sin m iI t cos sin cos sin mmm m I ILtIRt t tC
Z sin m di qLRi tdt C sin m iI t cos m diItdt cos m I qt ZSubstitute
PHY2054: Chapter 21
7General Solution for RLC Circuit (2)
Expand sin & cos expressions
Collect sin
t&cos tterms separatelyThese equations can be solved for I
m and (next slide)1/ cos sin 0
1/ sin cos
mmm LC RIL C IR
Z ZI IH sin sin cos cos sin cos cos cos sin sintt t ttt I Z IZIZ IHigh school trig!
cos tterms sin tterms cos sin cos sin mmm m I ILtIRt t tC
ZPHY2054: Chapter 21
8Solve for
and I m R, X L , X C and Z have dimensions of resistanceThis is where
, X L , X C and Z come from!General Solution for RLC Circuit (3)
1/tan LC XXLC R R mm I Z 22LC ZRXX L XL 1/ C XC
Inductive "reactance"
Capacitive "reactance"
Total "impedance"
PHY2054: Chapter 21
9AC Source and RLC Circuits
tan mm LC IZ XX RPhase angleMaximum current
= angle that current "lags" applied voltage 2 1/ L C XL f XCInductive reactance
Capacitive reactance
22LCZRXX
Total impedance
PHY2054: Chapter 21
10What is Reactance?
Think of it as a frequency-dependent resistance
Shrinks with increasing
1 C XC L X L R X RGrows with increasing
Independent of
PHY2054: Chapter 21
11Pictorial Understanding of Reactance
tan LC XX R 22LCZRXX cos RZ
PHY2054: Chapter 21
12 Summary of Circuit Elements, Impedance, Phase Angles 22LCZRXX tan LC XX R