Resistance and inductance series circuit, how to find the total voltage of the circuit?

The series circuit current is equal, the resistance voltage phase is the same as the current, and the inductance voltage phase is 90 degrees ahead of the current. Take the current as the polar axis to establish the coordinate system, draw ur and UL, and you can see that u = root (UR2 + UL2)

What does it mean that the voltage on the pure capacitor is 90 degrees ahead of the current?

That's the opposite! The current on the pure capacitor is 90 degrees ahead of the voltage!
A capacitor is a charging and energy storage element. It charges and discharges continuously in AC circuit. However, in each cycle, the initial charging current reaches the maximum value first, and the maximum voltage will wait until the end of charging! Therefore, the maximum current is always ahead of the maximum voltage! A complete cycle of three-phase AC power is 360 degrees! For each phase difference angle of 120 degrees, the lead current of the capacitor is 90 degrees ahead of the single phase!
The characteristic of inductance is opposite to that of capacitance!

How does the lead lag relationship between voltage and current phases work

When there is an inductor, the energy consumption is not proportional to the voltage and current of the load

Sine voltage U (T) = 50cos (120 π T + 210 °) V

As for this, it's very simple. First, you can go to encyclopedia to find the definition of effective value and initial phase! Effective value (sine and cosine) = peak value (root sign 2), and initial phase is 210 degrees

How to measure voltage, current and resistance with Multimeter

Correct use of multimeter
Multimeter, also known as multi-purpose meter, tri-purpose meter and multi-purpose meter, is a multi-functional and multi range measuring instrument. Generally, multimeter can measure DC current, DC voltage, AC voltage, resistance and audio level, and some can also measure AC current, capacitance, inductance and some parameters of semi conductor (such as β)
1. Structure of multimeter (Model 500)
The multimeter consists of meter head, measuring circuit and transfer switch
(1) Meter head: it is a magnetoelectric DC ammeter with high sensitivity. The main performance indexes of the multimeter basically depend on the performance of the meter head. The sensitivity of the meter head refers to the DC current value flowing through the meter head when the meter head pointer deflects at full scale. The smaller the value is, the higher the sensitivity of the meter head is. The greater the internal resistance when measuring voltage is, the better the performance will be, Their functions are as follows: the first one (from top to bottom) is marked with R or Ω, which indicates the resistance value. When the transfer switch is in ohm gear, the scale mark is read. The second one is marked with ∽ and VA, which indicates the AC, DC voltage and DC current value. When the transfer switch is in AC, DC voltage or DC current gear, and the range is in other positions except AC 10V, The third one is marked with 10V, indicating the AC voltage value of 10V. When the transfer switch is in the AC and DC voltage range and the AC voltage range is 10V, the third one is marked with DB, indicating the audio level
(2) Measuring line
The measuring circuit is used to convert all kinds of measured current into a small DC current suitable for meter measurement. It is composed of resistance, semiconductor components and battery
It can change all kinds of measured (such as current, voltage, resistance, etc.) and different measuring ranges into a certain amount of small DC current after a series of processing (such as rectification, shunt, voltage division, etc.) and send it to the meter for measurement
(3) Transfer switch
Its function is to select different measuring circuits to meet the measurement requirements of different types and ranges. Generally, there are two transfer switches with different gears and ranges
2. Symbol meaning
(1) ∽ denotes AC / DC
(2) V-2.5kv 4000 Ω / V indicates that the sensitivity is 4000 Ω / V for AC voltage and 2.5KV DC voltage
(3) A - V - Ω indicates the measurable current, voltage and resistance
(4) 45-65-1000hz means that the frequency range is below 1000Hz, and the standard power frequency range is 45-65hz
(5) 2000 Ω / V DC means the sensitivity of DC gear is 2000 Ω / v
The symbols on the clamp watch and dial are similar to the above symbols (because of the wrong format of other symbols, it is not possible to write "indicating magnetoelectric rectification type instrument with mechanical reaction force", "indicating three-stage external magnetic field" and "indicating horizontal placement")
3. Use of multimeter
(1) Be familiar with the meaning of each symbol on the dial and the main function of each knob and selection switch
(2) Carry out mechanical zero adjustment
(3) According to the type and size of the measured, select the gear and range of the transfer switch, and find out the corresponding scale line
(4) Select the position of the probe socket
(5) Measuring voltage: when measuring voltage (or current), you should choose a good range. If you use a small range to measure a large voltage, you will burn the meter. If you use a large range to measure a small voltage, the pointer deflection is too small to read. The selection of range should try to make the pointer deflection to about 2 / 3 of the full scale. If you do not know the measured voltage in advance, you should select the highest range gear, Then gradually reduce to the appropriate range
A. measurement of AC voltage: put one change-over switch of the multimeter in the AC and DC voltage range, and the other change-over switch in the appropriate range of AC voltage. The two probes of the multimeter can be connected in parallel with the circuit or load under test
B measurement of DC voltage: put one change-over switch of the multimeter in the AC and DC voltage range, the other change-over switch in the appropriate range of DC voltage, and connect the "+" probe (red probe) to the high potential and the "-" probe (black probe) to the low potential, that is, let the current flow in from the "+" probe and out from the "-" probe, It is easy to bend the pointer
(6) Current measurement: when measuring DC current, place one transfer switch of the multimeter at the DC current gear, and the other transfer switch at the appropriate range of 50ua to 500mA. The current range selection and reading method are the same as voltage. When measuring DC current, the circuit must be disconnected first, and then the multimeter shall be connected in series to the circuit to be measured according to the direction of current from "+" to "-", If the multimeter is connected in parallel with the load by mistake, the internal resistance of the meter head is very small, which will cause a short circuit and burn the instrument
Actual value = indicated value × measuring range / full deviation
(7) Measuring resistance: when measuring resistance with a multimeter, it should be done according to the following methods:
A select the appropriate ratio gear. The scale mark of Ohm gear of multimeter is uneven, so the selection of ratio gear should make the pointer stay in the thinner part of the scale mark, and the closer the pointer is to the middle of the scale, the more accurate the reading is. Generally, the pointer should be between 1 / 3 and 2 / 3 of the scale
B ohm zero adjustment. Before measuring resistance, two probes should be short circuited, and the "ohm (Electrical) zero adjustment knob" should be adjusted at the same time, so that the pointer just points to the zero position on the right side of the ohm scale line. If the pointer can not be adjusted to the zero position, it means that the battery voltage is insufficient or there is a problem in the instrument. In addition, Ohm zero adjustment should be carried out again every time the multiplier gear is changed, so as to ensure accurate measurement
C reading: the reading of the meter multiplied by the multiplying factor is the resistance value of the measured resistance
(8) Precautions
A when measuring current and voltage, it is not allowed to change the measuring range with electricity
B when selecting the measuring range, the larger one should be selected first, and then the smaller one, so as to make the measured value close to the measuring range as far as possible
When measuring the resistance, it is not allowed to measure the resistance on line. Because the multimeter is powered by the internal battery when measuring the resistance, if the resistance is measured on line, it is equivalent to connecting an additional power supply, which may damage the meter head
D. after use, the transfer switch should be in the maximum or neutral position of AC voltage
4. Digital multimeter
Now, the digital measuring instrument has become the mainstream, there is a trend to replace the analog instrument. Compared with the analog instrument, the digital instrument has high sensitivity, high accuracy, clear display, strong overload capacity, easy to carry, and easier to use. The following takes vc9802 digital multimeter as an example to briefly introduce its use methods and precautions
(1) How to use it
A before use, read the relevant instructions carefully and be familiar with the functions of power switch, range switch, Jack and special socket
B turn the power switch to the on position
C measurement of AC and DC voltage: set the range switch to the appropriate range of DCV (DC) or ACV (AC) as required, insert the red probe into the V / Ω hole, insert the black probe into the com hole, and connect the probe with the measured line in parallel, the reading will be displayed
D measurement of AC and DC current: set the range switch to the appropriate range of DCA (DC) or ACA (AC), insert the red probe into Ma hole (< 200mA) or 10A hole (> 200mA), insert the black probe into com hole, and connect the multimeter in series in the circuit under test. When measuring the DC flow, the digital multimeter can automatically display the polarity
E resistance measurement: set the range switch to the appropriate range of Ω, insert the red probe into the V / Ω hole, and insert the black probe into the com hole. If the measured resistance exceeds the maximum value of the selected range, the multimeter will display "1", and a higher range should be selected. When measuring resistance, the red probe is positive and the black probe is negative, which is just opposite to the pointer multimeter, When measuring transistor, electrolytic capacitor and other polar components, we must pay attention to the polarity of the probe
(2) . precautions for use
A if it is impossible to estimate the measured voltage or current in advance, it is necessary to first turn it to the highest range gear for measurement, and then gradually reduce the range to the appropriate position according to the situation. After the measurement, turn the range switch to the highest voltage gear and turn off the power supply
B at full range, the meter only displays the digit "1" at the highest position, and other bits disappear. At this time, a higher range should be selected
C when measuring voltage, the digital multimeter should be connected in parallel with the circuit under test. When measuring current, it should be connected in series with the circuit under test. When measuring direct flow, it is not necessary to consider the positive and negative polarity
D when the AC voltage block is misused to measure the DC voltage, or the DC voltage block is misused to measure the AC voltage, the display will show "000", or the number on the low position will jump
E it is forbidden to change the measuring range when measuring high voltage (above 220 V) or large current (above 0.5 A), so as to prevent arcing and burning switch contacts
F when "" or "batt" or "low bat" is displayed, the battery voltage is lower than the working voltage

Error analysis of voltage and current measurement experiment with Multimeter

An introductory question: if a circuit with inductive reactance can measure the voltage and current at a certain frequency with a multimeter, then the voltage / current ratio is zero
Is it equal to the impedance at this frequency?

If the multimeter is accurate, the voltage / current is equal to the impedance at this frequency

How to measure voltage and current with Multimeter?
When measuring the voltage and current with a multimeter, do you need to remove the battery in the meter? Do you need to adjust to zero? Also, when measuring the capacitance, I found that the pointer would deflect to the right and return to zero. Why?

If it is a digital multimeter, insert the probe into the voltage gear, adjust the measuring mode gear to the voltage gear, and measure the voltage directly. The current gear is similar, insert the probe into the current gear, adjust the measuring mode gear to the appropriate current gear, and measure in series in the circuit
Pointer type multimeter has never been used, do not know what special requirements
When measuring the capacitance, I found that the pointer would deflect to the right and then return to zero. I should have learned in high school that the voltage at both ends of the capacitor can't change suddenly. When measuring the voltage of the multimeter, there is actually a small current charging it. After charging, it will return to zero

Given that the effective value of sinusoidal voltage is 200V, the frequency is 100Hz, and the initial phase angle is, the instantaneous value expression u =

If the initial phase angle is a, the instantaneous

Resistance and inductance series circuit, how to find the total voltage of the circuit?