Question

NAME RESISTORS IN SERIES CIRCUITS Construct the circuit Figure using The Circuit Construction KCK) simulation at the Presite - 400, R; -90 and R, -120 . Use the ammeter moving it to take readings in the different places as seen in Figure 1A. A As and Ar). Then use the voltmeter to take voltage readings Ms. V. Vand V. Calculate Rusing Ohms Law (Vol for the total resistance in last column. Adjust-20.0V.FI out Table 1 www Table 1 Resistor Gm Voltagel Current A) Resistance) 130 cm Total VT reading At reading RTVTAT How is the total resistance related to the individual resistances? Total current to the individual currents? Total voltage to the individual voltages? RESISTORS IN PARALLEL CIRCUITS Wire the circuit in Figure 2 (R. - 400 R - 80. and Ry - 120 Take readings in different places shown in Figure 2 by moving the meters. Fill out Table 2. Calculate total resistance using Chn's Law for the last column Adjust, 20:0V. M. Current Resistance 2 www. Resistor Voltage 46mm 80ms 120 ohms TOES VT reading 2 www AT reading RT-VT/T Figure 2 a. How is the total resistance related to the individual resistances? Explain what you think is haine

Answer 1

Resistors in series:

R₁ = 40 Ω ; R₂ = 80 Ω ; R₃ = 120 Ω ; V_bat = 20 V

Total resistance of the series combination, R_s = R₁ + R₂ + R₃ = 40 + 80 + 120 = 240 Ω

Current in the circuit, I = V_bat/ R_s = 20/240 = 0.0833 A

Voltage across R₁ is V₁ = I R₁ = 20/240 x 40 = 3.33 V

Voltage across R₂ is V₂ = I R₂ = 20/240 x 80 = 6.66 V

Voltage across R₃ is V₃ = I R₃ = 20/240 x 120 = 10 V

Resistor	Voltage in V	Current in A	Resistance in Ω
40 Ω	3.33	0.0833	40 Ω
80 Ω	6.66	0.0833	80 Ω
120 Ω	10.	0.0833	120 Ω

Resistors in parallel:

R₁ = 40 Ω ; R₂ = 80 Ω ; R₃ = 120 Ω ; V_bat = 20 V

If R_p is the total resistance of the parallel combination,

1/ R_p = 1/ R₁ +1/ R₂ +1/ R₃ = 1/40 +1/80 +1/120

R_p = 21.81 Ω

Current through resistor R₁ is I₁ = V_bat/ R₁ = 20/40 = 0.5 A

Current through resistor R₂ is I₂ = V_bat/ R₂= 20/80 = 0.25 A

Current through resistor R₃ is I₃ = V_bat/ 3₁ = 20/120 = 0.166 A

Total current in the circuit, I = V_bat/ R_p = 20 /22.91 = 0.873 A

Resistor	Voltage in V	Current in A	Resistance in Ω
40 Ω	20	0.5	40 Ω
80 Ω	20	0.25	80 Ω
120 Ω	20	0.166	120 Ω

Combination circuit:

R₁ = 40 Ω ; R₂ = 80 Ω ; R₃ = 120 Ω ; V_bat = 20 V

In the circuit given, R₂ and R₃ are in parallel. Their effective resistance, R_p = R₂ R₃/( R₂ + R₃)

R_p = 80 x 120/( 80 + 120) = 48 Ω

R₁ and R_p are in series and the total resistance of the circuit, R = R₁ + R_p = 40 + 48 = 88 Ω

Current in the circuit, I = V_bat /R= 20/88 = 0.227 A

Voltage across R₁ is V₁ = I R₁ = 0.227 x 40 = 9.08 V

Voltage across R₂ is V₂ = I R_p = 0.227 x 48 = 10.89 V

Voltage across R₃ is V₃ = I R_p = 0.227 x 48 = 10.89 V

Current through R₂ = R₃= 0.227/2 = 0.1135

Resistor	Voltage in V	Current in A	Resistance in Ω
40 Ω	9.08	0.227	40 Ω
80 Ω	10.89	0.1135	80 Ω
120 Ω	10.89	0.1135	120 Ω