**Experiment No.: **4

**Experiment Name:**

Use of Voltmeter, Ammeter, Wattmeter to Determine Active, Reactive and Apparent Power

Consumed in Given R-L-C Series Circuit and Draw Phasor Diagram.

**Objective:**

- To use voltmeter, ammeter, wattmeter to determine active, reactive and apparent power

consumed in given R-L-C series circuit. - To draw the phasor diagram of that circuit.

**Theory:**

Let V volts (rms) be applied to an R-L-C series circuit and the current flowing through the circuit be I amps. The impedance Z=V/I. If voltage across resistor is V_{R} then R=V_{R}/I

If voltage across inductor is _{V r,L, }the impedance of the inductor coil is given by

V_{r},_{L}/I=√(r^{2}+X_{L}^{2})

Again the voltage across the resistance R and coil V_{R, L}, then

V_{r},_{L}/I=√((R+r)^{2}+X_{L}^{2} )

From the above two equation the value of R and X_{L }can be found out. If the voltage across the capacitor is V_{C} then the reactance of the capacitor is given by X_{C}=V_{C}/I. hence the value of capacitance C=1/ωV_{C} where ω=2πf is the angular frequency. the power factor is given by (R+r)/Z. If V_{C}>V_{L}, The pf is leading otherwise lagging.

The power consumed P=I^{2}(R+r) or VI cos Ø

**Circuit Diagram:**

**Procedure:**

- The circuit is connected as shown in the circuit diagram with resistor, the inductor coil and capacitor in series.
- The variac is adjusted to zero output position and the circuit is switched on.
- A suitable voltage is applied from the variac so that a reasonable current flows through the circuit. The output voltage of the variac and voltage across the resistor, inductor and the capacitor are noted along with the current.
- Different readings are taken by varying voltage from the variac.
- Readings are noted from the data sheet.

**Observation Table:**

Sl no | Voltage (V) | Current (mA) | Frequency (kHz) | R (Ω) | L (mH) | C (nF) | V_{R} (V) | V_{R} (V) | V_{C} (V) | PF = cos Ø | Active power (mW) [VIcosØ] | Reactive power (mVAR) [VIsinØ] | Apparent power (mVA) [VI] |

1. | 5.02 | 9.09 | 13.05 | 546 | 7.75 | 22.08 | 4.67 | 4.22 | 4.2 | 0.98 | 44.71 | 9.034 | 45.62 |

**Calculation:**

X_{L} = 2πfL = 2π×13.05×10^{3}×7.75×10^{-3}= 635.46 Ω

X_{C} = 1/2πfC = 1/(2π×13.05×10^{3}×22.08×10^{-9})= 552.34 Ω

cos Ø = R/Z = R/√(R^{2}+(X_{L} – X_{C})^{2}) = 546/√(546^{2}+(635.46 – 552.34)^{2}) = 546/552.29 = 0.98 lag

Active power = VIcosØ = 5.02×9.09×10^{-3}×0.98 = 44.71 mW

Rective power = VIsinØ = 5.02×9.09×10^{-3}×0.198 = 9.034 mVAR

Apparent power = VI = 5.02×9.09×10^{-3} = 45.62 mVA

**Phasor Diagram: **

**Apparatus Used:**

Sl. No. | Name of the apparatus | Quantity | Specification | Makes name |

1. | Single phase variac | 1 | 230/0-270 V ac | |

2. | LCR Trainer Kit | 1 | Sushama Electronics | |

3. | Digital Multimeter | 3 | 0-750 V, 10 A | Akademika |

4. | Wattmeter | 1 | Digital | |

5. | LCR Meter | 1 | Digital | Metravi |

6. | Connecting Probes | 10 | RGP-2 |

**Remarks:**

- The phasor diagram of different voltage and current for at least two observation are drawn in the graph paper.
- The value of power factor and magnitude of the supplied voltage are found from phasor diagram.

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