Applying electrical quantities is fundamental in biomedical engineering, where precise measurement and understanding of electrical units ensure the safe and effective design, maintenance, and troubleshooting of medical devices. In Kenya’s healthcare facilities, from county hospitals to research laboratories, biomedical engineers rely on standardized units to communicate and apply electrical concepts accurately. This chapter begins by establishing the meaning and application of the International System of Units (SI units), which is critical for consistent electrical measurement and analysis in biomedical contexts.

1.1 The meaning of SI unit

The International System of Units (SI) forms the backbone of all electrical measurements in biomedical engineering. It ensures that quantities such as voltage, current, resistance, and capacitance are universally understood and applied. Mastery of SI units is essential for Kenyan biomedical engineers working with diagnostic equipment, patient monitoring systems, and therapeutic devices where precise electrical parameters affect performance and safety.

1.1.1 Defining the SI unit and its role in biomedical engineering

The SI unit is the globally accepted standard for expressing physical quantities, including electrical measurements. For biomedical engineers, using SI units guarantees consistency when calibrating instruments, interpreting sensor outputs, and communicating findings across multidisciplinary teams.

$$\text{SI unit} = \text{standard unit agreed internationally for each physical quantity}$$

Worked Examples

Example 1: A biomedical engineer needs to record the voltage output of an ECG machine. The voltage is measured as 1 millivolt. Express this voltage in the SI unit.

Given: Voltage \(V = 1 \text{ mV}\)
SI unit for voltage is volts (V).

$$V = 1 \text{ mV} = 1 \times 10^{-3} \text{ V}$$

Answer: 0.001 V

Example 2: A heart rate monitor uses a current of 5 microamperes. Convert this current to amperes.

Given: Current \(I = 5 \mu A\)
SI unit for current is amperes (A).

$$I = 5 \times 10^{-6} \text{ A}$$

Answer: 0.000005 A

Example 3: A bioimpedance device has a resistance of 2 kilo-ohms. Express this resistance in ohms.

Given: Resistance \(R = 2 \text{ k}\Omega\)
SI unit for resistance is ohms (\(\Omega\)).

$$R = 2 \times 10^{3} \Omega$$

Answer: 2000 \(\Omega\)

Example 4: A capacitance sensor reads 0.25 microfarads. Convert this to farads.

Given: Capacitance \(C = 0.25 \mu F\)
SI unit for capacitance is farads (F).

$$C = 0.25 \times 10^{-6} F$$

Answer: 2.5 \times 10^{-7} F

Example 5: A pulse oximeter applies a voltage of 12 volts across its sensors. Express this voltage in millivolts.

Given: Voltage \(V = 12 V\)
Convert volts to millivolts (mV).

$$V = 12 \times 10^{3} \text{ mV}$$

Answer: 12000 mV

1.1.2 Recognizing base SI units and derived units in electrical quantities

Electrical quantities are expressed using base SI units such as meters, kilograms, seconds, and amperes. Derived units combine base units to quantify properties like voltage and resistance. Understanding these units is crucial for biomedical engineers to interpret device specifications and ensure correct device operation.

$$\text{Voltage (V)} = \frac{\text{kg} \times \text{m}^2}{\text{s}^3 \times \text{A}}$$

$$\text{Resistance} (\Omega) = \frac{\text{kg} \times \text{m}^2}{\text{s}^3 \times \text{A}^2}$$

Worked Examples

Example 1: Express voltage in terms of base SI units.

Given: Voltage \(V\)
Formula for voltage in base SI units:

$$V = \frac{kg \times m^{2}}{s^{3} \times A}$$

Answer: Voltage is measured in kilograms times meters squared per second cubed per ampere.

Example 2: Express resistance in base SI units.

Given: Resistance \(R\)
Formula for resistance in base units:

$$R = \frac{kg \times m^{2}}{s^{3} \times A^{2}}$$

Answer: Resistance is measured in kilograms times meters squared per second cubed per ampere squared.

Example 3: Calculate the derived SI unit for capacitance in terms of base units.

Given: Capacitance \(C\)
Capacitance unit (farad) in base units:

$$C = \frac{s^{4} \times A^{2}}{kg \times m^{2}}$$

Answer: Capacitance is seconds to the fourth power times amperes squared per kilogram meter squared.

Example 4: Express power (watts) in base SI units.

Given: Power \(P\)
Power unit (watt) in base units:

$$P = \frac{kg \times m^{2}}{s^{3}}$$

Answer: Power is kilograms times meters squared per second cubed.

Example 5: Express energy (joule) in base SI units.

Given: Energy \(E\)
Energy unit (joule) in base units:

$$E = \frac{kg \times m^{2}}{s^{2}}$$

Answer: Energy is kilograms times meters squared per second squared.

1.1.3 Converting electrical quantities using SI prefixes

SI prefixes simplify expressing very large or very small electrical quantities. Biomedical engineers in Kenya often need to convert between units such as milliamperes and amperes or kilovolts and volts when calibrating medical equipment or analyzing signals.

$$\text{Value with prefix} = \text{Value without prefix} \times 10^{n}$$

Where \(n\) depends on the prefix.

Worked Examples

Example 1: Convert 3.5 milliamperes to amperes.

Given: Current \(I = 3.5 \text{ mA}\)

$$I = 3.5 \times 10^{-3} A$$

Answer: 0.0035 A

Example 2: Convert 0.007 kiloohms to ohms.

Given: Resistance \(R = 0.007 \text{ k}\Omega\)

$$R = 0.007 \times 10^{3} \Omega$$

$$R = 7 \Omega$$

Answer: 7 \(\Omega\)

Example 3: Convert 250 microvolts to volts.

Given: Voltage \(V = 250 \mu V\)

$$V = 250 \times 10^{-6} V$$

$$V = 0.00025 V$$

Answer: 0.00025 V

Example 4: Convert 5 volts to millivolts.

Given: Voltage \(V = 5 V\)

$$V = 5 \times 10^{3} \text{ mV}$$

Answer: 5000 mV

Example 5: Convert 0.02 farads to microfarads.

Given: Capacitance \(C = 0.02 F\)

$$C = 0.02 \times 10^{6} \mu F$$

$$C = 20000 \mu F$$

Answer: 20000 \(\mu F\)

1.1.4 Applying SI units in biomedical engineering measurements and instrumentation

Biomedical engineers use SI units to measure and interpret electrical parameters in devices such as defibrillators, EEG machines, and pacemakers. Accurate application of SI units ensures device safety, regulatory compliance, and reliable patient data interpretation.

$$\text{Electrical Quantity} = \text{Measured Value} \times \text{SI Unit}$$

Worked Examples

Example 1: An EEG machine records a voltage of 50 microvolts. Express this voltage in volts and state its significance.

Given: Voltage \(V = 50 \mu V\)

$$V = 50 \times 10^{-6} V$$

$$V = 0.00005 V$$

Answer: 0.00005 V; this low voltage is typical for brain electrical activity measurements.

Example 2: A pacemaker delivers a current of 2 milliamperes. Convert this current to amperes and explain its application.

Given: Current \(I = 2 \text{ mA}\)

$$I = 2 \times 10^{-3} A$$

Answer: 0.002 A; this current level is critical for stimulating cardiac muscle without tissue damage.

Example 3: A defibrillator charges a capacitor of 150 microfarads. Convert capacitance to farads.

Given: Capacitance \(C = 150 \mu F\)

$$C = 150 \times 10^{-6} F$$

$$C = 0.00015 F$$

Answer: 0.00015 F; capacitance affects the energy delivered during defibrillation.

Example 4: A biosensor has a resistance of 500 ohms. Express this resistance in kilo-ohms.

Given: Resistance \(R = 500 \Omega\)

$$R = \frac{500}{1000} k\Omega$$

$$R = 0.5 k\Omega$$

Answer: 0.5 k\(\Omega\); resistance impacts sensor sensitivity and signal quality.

Example 5: A medical imaging device operates at power of 100 watts. Express power in kilowatts.

Given: Power \(P = 100 W\)

$$P = \frac{100}{1000} kW$$

$$P = 0.1 kW$$

Answer: 0.1 kW; power consumption is important for device efficiency and heat management.

Chapter Summary

This chapter introduced the concept of the SI unit as the standard system of measurement used internationally for electrical quantities. It detailed the specific SI units for different electrical parameters such as current, voltage, resistance, and power, providing a clear understanding of their fundamental measures. The chapter then explained Ohm's law, establishing the relationship between voltage, current, and resistance in electrical circuits. It included practical calculations involving these parameters, demonstrating how to compute power, current, voltage, and resistance in various scenarios. Finally, the chapter covered the common instruments used to measure electrical quantities, such as voltmeters, ammeters, and ohmmeters, emphasizing their roles in accurate electrical measurement and circuit analysis. This comprehensive overview equips students with foundational knowledge necessary for electrical circuit analysis and practical application.