By the end of this chapter, you will be able to:
- Identify common electrical quantities and their units using the SI system correctly.
- Perform accurate calculations involving electrical quantities using the right formulas.
- Recognize electrical measuring instruments according to IEC standards.
Mastering these skills will help you work confidently and safely with electrical systems in real-world trade settings.
Applying electrical quantities is fundamental in biomedical engineering, especially in Kenya where medical device performance and patient safety depend on precise electrical measurements. Understanding how electrical quantities are measured, quantified, and applied ensures accurate diagnostics, effective therapeutic devices, and compliance with international standards. This chapter introduces the International System of Units (SI units) as the universal language for electrical quantities, enabling biomedical engineers to communicate, calculate, and troubleshoot electrical parameters reliably across diverse healthcare environments.
The International System of Units (SI) is crucial for biomedical engineers in Kenya to standardize measurements of electrical quantities such as current, voltage, resistance, and power. These units provide consistency when designing, calibrating, and maintaining biomedical instruments like ECG machines, defibrillators, and infusion pumps. Mastery of SI units facilitates accurate data interpretation and ensures compatibility with global biomedical standards.
SI units form the globally accepted measurement system based on seven fundamental units from which all other units derive. The SI system supports clear, consistent, and unambiguous communication of physical quantities, essential for biomedical device design and clinical measurements.
The seven fundamental SI units relevant to electrical quantities include the ampere for electric current, the volt for electric potential, the ohm for resistance, and the watt for power.
$$ \text{SI Units are defined such that derived units} = \text{combinations of fundamental units} $$
Example 1: Determine the SI unit for electric current used in a cardiac pacemaker circuit.
Given: Electric current
$$ \text{Unit of current} = \text{ampere (A)} $$
Answer: 1 ampere (A)
Example 2: Identify the SI unit for voltage measured in an EEG machine.
Given: Electric potential difference
$$ \text{Unit of voltage} = \text{volt (V)} $$
Answer: 1 volt (V)
Example 3: Express the SI unit for resistance in a bioimpedance analyzer.
Given: Resistance
$$ \text{Unit of resistance} = \text{ohm} = \frac{\text{volt}}{\text{ampere}} = \Omega $$
Answer: 1 ohm (Ω)
Example 4: Calculate the power unit used in an X-ray tube.
Given: Power
$$ \text{Unit of power} = \text{watt} = \text{volt} \times \text{ampere} = \text{W} $$
Answer: 1 watt (W)
Example 5: Derive the SI unit for capacitance used in defibrillator capacitors.
Given: Capacitance
$$ \text{Unit of capacitance} = \text{farad} = \frac{\text{coulomb}}{\text{volt}} = \text{F} $$
Answer: 1 farad (F)
Electrical quantities often require derived SI units formed by combining fundamental units. These derived units simplify calculations and standardize measurements in biomedical devices.
$$ \text{Resistance} (R) = \frac{\text{Voltage} (V)}{\text{Current} (I)} = \Omega $$
$$ \text{Power} (P) = \text{Voltage} (V) \times \text{Current} (I) = W $$
Example 1: Calculate resistance in a nerve conduction study circuit with voltage 12 V and current 3 A.
Given: \(V = 12\,V\), \(I = 3\,A\)
$$ R = \frac{V}{I} $$
$$ R = \frac{12}{3} $$
$$ R = 4\,\Omega $$
Answer: 4 ohms (Ω)
Example 2: Determine power consumption for an infusion pump operating at 24 V and 0.5 A.
Given: \(V = 24\,V\), \(I = 0.5\,A\)
$$ P = V \times I $$
$$ P = 24 \times 0.5 $$
$$ P = 12\,W $$
Answer: 12 watts (W)
Example 3: Find the resistance of electrodes with voltage 5 V and current 0.01 A in an ECG machine.
Given: \(V = 5\,V\), \(I = 0.01\,A\)
$$ R = \frac{V}{I} $$
$$ R = \frac{5}{0.01} $$
$$ R = 500\,\Omega $$
Answer: 500 ohms (Ω)
Example 4: Compute power dissipated by a heating element in a sterilization device with 220 V and 2.5 A.
Given: \(V = 220\,V\), \(I = 2.5\,A\)
$$ P = V \times I $$
$$ P = 220 \times 2.5 $$
$$ P = 550\,W $$
Answer: 550 watts (W)
Example 5: Calculate resistance of a sensor wire with voltage 0.9 V and current 0.03 A.
Given: \(V = 0.9\,V\), \(I = 0.03\,A\)
$$ R = \frac{V}{I} $$
$$ R = \frac{0.9}{0.03} $$
$$ R = 30\,\Omega $$
Answer: 30 ohms (Ω)
SI units use prefixes to express very large or very small quantities, essential in biomedical engineering where electrical signals can range from microvolts to kilovolts.
Common prefixes include micro (\(\mu\)), milli (m), kilo (k), and mega (M).
$$ \text{Value with prefix} = \text{Value} \times 10^{\text{power}} $$
Example 1: Convert 5 milliamperes to amperes for a pacemaker current.
Given: \(5\,mA\)
$$ 1\,mA = 10^{-3} A $$
$$ 5\,mA = 5 \times 10^{-3} A $$
$$ = 0.005\,A $$
Answer: 0.005 amperes (A)
Example 2: Express 0.002 volts in millivolts for EEG signal measurement.
Given: \(0.002\,V\)
$$ 1\,mV = 10^{-3} V $$
$$ 0.002\,V = \frac{0.002}{10^{-3}} mV $$
$$ = 2\,mV $$
Answer: 2 millivolts (mV)
Example 3: Convert 3 kiloohms to ohms for electrode resistance.
Given: \(3\,k\Omega\)
$$ 1\,k\Omega = 10^{3} \Omega $$
$$ 3\,k\Omega = 3 \times 10^{3} \Omega $$
$$ = 3000\,\Omega $$
Answer: 3000 ohms (Ω)
Example 4: Express 0.000045 farads in microfarads for capacitor value.
Given: \(0.000045\,F\)
$$ 1\,\mu F = 10^{-6} F $$
$$ 0.000045\,F = \frac{0.000045}{10^{-6}} \mu F $$
$$ = 45\,\mu F $$
Answer: 45 microfarads (μF)
Example 5: Convert 1.5 megawatts to watts for hospital power supply rating.
Given: \(1.5\,MW\)
$$ 1\,MW = 10^{6} W $$
$$ 1.5\,MW = 1.5 \times 10^{6} W $$
$$ = 1,500,000\,W $$
Answer: 1,500,000 watts (W)
In biomedical engineering, precise measurement of electrical quantities using SI units ensures device accuracy and patient safety. Devices such as pulse oximeters, EEG machines, and defibrillators rely on standardized units for calibration and operation.
Electrical quantities measured in SI units include:
Example 1: Calculate the current drawn by a defibrillator operating at 200 V and consuming 1000 W.
Given: \(V = 200\,V\), \(P = 1000\,W\)
$$ P = V \times I $$
$$ I = \frac{P}{V} $$
$$ I = \frac{1000}{200} $$
$$ I = 5\,A $$
Answer: 5 amperes (A)
Example 2: Find voltage across a resistor of 50 Ω when current is 0.2 A in an ECG machine.
Given: \(R = 50\,\Omega\), \(I = 0.2\,A\)
$$ V = I \times R $$
$$ V = 0.2 \times 50 $$
$$ V = 10\,V $$
Answer: 10 volts (V)
Example 3: Determine power dissipated by a heater in a sterilizer with resistance 40 Ω and current 3 A.
Given: \(R = 40\,\Omega\), \(I = 3\,A\)
$$ P = I^{2} \times R $$
$$ P = 3^{2} \times 40 $$
$$ P = 9 \times 40 $$
$$ P = 360\,W $$
Answer: 360 watts (W)
Example 4: Calculate resistance in a bioimpedance device with voltage 1.2 V and current 0.04 A.
Given: \(V = 1.2\,V\), \(I = 0.04\,A\)
$$ R = \frac{V}{I} $$
$$ R = \frac{1.2}{0.04} $$
$$ R = 30\,\Omega $$
Answer: 30 ohms (Ω)
Example 5: Find current in a sensor circuit with power 0.5 W and voltage 5 V.
Given: \(P = 0.5\,W\), \(V = 5\,V\)
$$ P = V \times I $$
$$ I = \frac{P}{V} $$
$$ I = \frac{0.5}{5} $$
$$ I = 0.1\,A $$
Answer: 0.1 amperes (A)
Calculate the resistance of a biomedical electrode if the voltage across it is 9 V and the current flowing is 0.03 A. (4 marks)
A defibrillator draws a current of 4 A when operating at 220 V. Calculate the power consumption. (4 marks)
Convert 0.007 volts to millivolts. (3 marks)
An EEG sensor operates at 2 milliamperes current and 5 volts voltage. Find the power used. (4 marks)
A sterilizer heating element has a resistance of 60 Ω and a current of 5 A flows through it. Calculate the voltage across it and the power dissipated. (6 marks)
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Create a free accountThis chapter introduced the concept of the SI unit as the standard measurement system used in electrical engineering to ensure consistency and accuracy. It covered the SI units for various electrical parameters such as current, voltage, resistance, and power, providing a foundation for understanding their measurement and application. The chapter explained Ohm's law, which establishes the relationship between voltage, current, and resistance in an electrical circuit. Detailed calculations involving electrical parameters were demonstrated to enable practical problem-solving in real-world scenarios. The use of instruments for measuring electrical quantities was also discussed, highlighting the appropriate tools for current, voltage, resistance, and power measurement. Through these topics, students gained essential knowledge to apply electrical quantities effectively in engineering tasks.
A biomedical device draws a current of \(2\, \mathrm{A}\) when connected to a \(12\, \mathrm{V}\) power supply. Calculate the resistance of the device. (2 marks)
An ECG machine operates at a voltage of \(9\, \mathrm{V}\) and has a resistance of \(18\, \Omega\). Find the current flowing through the machine. (2 marks)
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