Basics of AC and DC Technology Manual 7 7.1 Series Connection of Voltage Sources Basics Ui1 Uo 1 U₁2 U0 2 = (11) Riges + pic. 7.1.1 Uo1, U02 Primary

Voltages R₁1, R₁2 U₁1, U₁2 U₁, U₂ Ri1 Ri 2 = Internal Resistances = Voltage Drop at Internal Resistance = Partial Voltages = = Total Voltage = Load Current = Load Resistance Whera Ril + Ri2 5 U₁ Uges IL R₁ By connecting more voltage sources in series, the total voltage is increased as follows: UGES = U01+ U02 U2 www.hera.de IL Uges Precondition is, that the poles of the voltage source are correctly connected, means positive pole of one voltage source to the negative pole of the second, etc. The internal resistances of the series connected voltage sources are added to a total internal resistance Ri ges: RL 48 If voltage sources in series connection are connected to load RL, then the current is depending on the primary voltage, the load current and the internal resistances of all voltage sources. Technical details are subject to change hera Laborsysteme GmbH, Hermann-Rapp-Str.40, DE-74572 Blaufelden Basics of AC and DC Technology Manual 7.2 IL = Tests Test Uo RL + Ri1 + Ri2 Required Materials: Connect the two voltage sources in series as explained above and determine the total voltage Uges. Connectors and Safety Leads ● 1x Multimeter Time: approx. 5 min. 0...30V - 15V Test 1: ground internally connected pic. 7.2.1 Aufbau Test Procedure: + U01 = +5V Answer: Z 1U02 = +15V + UGES Whera Set up the series connection for two voltage sources as shown in pic. 7.2.1. Set the voltage of the adjustable power supply to 5V. What is the total voltage Uges, if series connected? Technical details are subject to change hera Laborsysteme GmbH, Hermann-Rapp-Str.40, DE-74572 Blaufelden www.hera.de 499 Basics of AC and DC Technology Manual 8 8.1 Parallel Connection of Voltage Sources Basics 1₁ IL R₁1 = U01 To Riges U₁2 12 R₁2 pic. 8.1.1 U₁1, U₁2 = Voltage Drops at Internal Resistances U01, U02 = Primary Voltage R₁1, R₁2 11, 12 IL lo U₁2 = Internal Resistance = Partial Currents = Load Current U02 = Compensating Current = Terminal Voltage 1 U₁2 Ril Ri2 Ril + Ri2 2 If more voltage sources with same primary voltage are connected in parallel, the load current IL increases. For this the same type of poles needs to be connected, means positive pole to positive pole and vice versa. If the power supplies have different primary voltages there will be a compensating current lo between the poles. This current is depending on the differential voltage and the respective internal resistance. m The load current IL is depending on the load resistance R₁, the load resistance of each voltage source and the primary voltages. U01 Ri2+ U02 · Ril Ri1 R₁2 + Ri1 · RL + Ri2. RL . RL hera® The internal resistances are in parallel to each other, means the total internal resistance is calculated as follows: www.hera.de 50 Technical details are subject to change hera Laborsysteme GmbH, Hermann-Rapp-Str.40, DE-74572 Blaufelden Basics of AC and DC Technology Manual 8.2 Tests Test Connect two voltage sources in parallel and measure stated parameter for same primary voltages and different primary voltages. Do those measurements with and without load. ● Measuring parameters without load: voltage drops due to internal resistance U₁₁ and U₁2, compensating current lo, terminal voltage U₁2. Connectors and Safety Leads 2x Resistor 100 1x Resistor 1kQ 1x Multimeter Time: approx. 35 min. To Measuring parameters with load: voltage drops due to internal resistance U₁₁ and U₁2, partial currents ₁ and 12, load current IL, terminal voltage U₁2. Check your results for the load currents IL by calculation. Required Materials: ● R₁1=1000 Z U₁₁ 15V/20V pic. 8.2.1 Aufbau Test Procedure: U₁₁ R₁2=1000 U₁2 U02 15V m 1 U12 hera Ⓡ R₁=1KQ www.hera.de 51 Set up the circuit of two voltage sources in parallel according to pic. 8.2.1. For clearer measuring results of parameter U₁₁ and U₁2 the internal resistances of each voltage source is increased by 1000 resistor. Set the adjustable power supply to Uo1 = 15V (U01 = U02) for measurements with same primary voltages. For measurements of parameters with different primary voltages set the voltage to U01 = 20V. For current measurements the circuit needs to be disconnected at the marked positions. Fill your results in chart 8.2.1 and 8.2.2. Technical details are subject to change hera Laborsysteme GmbH, Hermann-Rapp-Str.40, DE-74572 Blaufelden Basics of AC and DC Technology Manual Same Primary Voltages (U₁₁ = U02 = 15V) non-load U₁₁ [V] U₁2 [V] chart 8.2.1 Belastung (1 k) U₁₁ [V] U₁2 [V] |U₁2 [V] l₁ [mA] 1₂ [mA] l₁ [mA] U₁2 [V] Different Primary Voltages (U₁₁ = 20V; U02 = 15V) non-load U₁₁ [V] U₁2 [V] U₁2 [V] lo [mA] chart 8.2.2 lo [mA] Load (1k0) U₁₁ [V] U₁2 [V] U₁2 [V] l₁ [mA] 1₂ [mA] l₁ [mA] Test: Calculate the compensating current for different primary voltages. Answer: Whera Calculate the load current for different primary voltages. Calculate the load currents for different primary voltages. How do the partial currents behave with same primary voltages? www.hera.de Ⓡ Technical details are subject to change hera Laborsysteme GmbH, Hermann-Rapp-Str.40, DE-74572 Blaufelden 52