What is the total conductance, measured in Siemens, of a circuit containing a 10Ω and a 20Ω resistor connected in parallel?

What is the total conductance, measured in Siemens, of a circuit containing a 10Ω and a 20Ω resistor connected in parallel?

• A. 0.05S
• B. 0.1S
• C. 0.15S
• D. 0.6S

Answer: (C)

To determine the total conductance of a circuit with resistors in parallel, you first calculate the individual conductances of each resistor. Conductance (G) is the reciprocal of resistance (R), expressed as: \[ G = \frac{1}{R} \] For the 10Ω resistor, the conductance is: \[ G_1 = \frac{1}{10Ω} = 0.1S \] For the 20Ω resistor, the conductance is: \[ G_2 = \frac{1}{20Ω} = 0.05S \] Next, the total conductance in a parallel circuit is the sum of the individual conductances: \[ G_{total} = G_1 + G_2 \] Substituting the calculated values: \[ G_{total} = 0.1S + 0.05S = 0.15S \] This results in a total conductance of 0.15 Siemens. Understanding this process is key for diagnosing and analyzing electrical systems in biomedical equipment, where knowledge of conductance assists in fault detection and equipment performance evaluations.

To determine the total conductance of a circuit with resistors in parallel, you first calculate the individual conductances of each resistor. Conductance (G) is the reciprocal of resistance (R), expressed as:

[ G = \frac{1}{R} ]

For the 10Ω resistor, the conductance is:

[ G_1 = \frac{1}{10Ω} = 0.1S ]

For the 20Ω resistor, the conductance is:

[ G_2 = \frac{1}{20Ω} = 0.05S ]

Next, the total conductance in a parallel circuit is the sum of the individual conductances:

[ G_{total} = G_1 + G_2 ]

Substituting the calculated values:

[ G_{total} = 0.1S + 0.05S = 0.15S ]

This results in a total conductance of 0.15 Siemens. Understanding this process is key for diagnosing and analyzing electrical systems in biomedical equipment, where knowledge of conductance assists in fault detection and equipment performance evaluations.