Design & Technology
Electronic calculations
You need to be able to calculate values such as power [power:
The rate at which energy is transferred or work is done, measured in
'W'. Power = work done ÷ time taken. ], resistance [resistance: The
opposition in an electrical component to the flow of electricity through
it. Resistance is measured in ohms. ], circuit output [output:
Whatever comes out of a system. In electronics, output components
deliver a circuit's end result, while the output of a component is the
size of electrical signal at its output terminal ], and current gain [gain:
the amount of amplification of the input voltage - ie how much bigger
the output voltage is compared to the input voltage ].
There are a number of formulae to help you with these
calculations, and you need to be familiar with these. You don't
necessarily need to learn them, as you will usually be given a
formula sheet in your exam.
Calculating power
Power is the rate of energy output, or work done by a component or
device.
Power (P) = voltage (V) x current (I)
 P = power (measured in watts, W)
 V = voltage (volts, V)
 I = current (amps, A)
Example
A resistor has a current of 0.025A flowing through it when it has a
voltage of 9V placed across its ends. Determine whether a resistor
with a 0.125W power rating will be able to handle the current value.
P=V x I = 9 x 0.025 = 0.225W
A resistor of 0.125 Watts would therefore be too low to handle the
0.025A current.
Calculating resistance
Resistors in series
The combined resistance [resistance: The opposition in an electrical
component to the flow of electricity through it. Resistance is measured
in ohms. ] of two resistors in series is the sum of the resistance values
of the two resistors in ohms. The formula is:-
R total = R1 + R2
 R total = combined resistance value (in ohms)
 R1 = value of resistance in first resistor (ohms)
 R2 = value of resistance in second resistor (ohms).
Example
Two resistors with resistance values 1.2 kilo-ohms (K) and 2.2 kiloohms (K) are connected in series. Determine the total resistance of
the network.
R total = R1+R2 = 1.2k + 2.2k = 3.4k
Resistors in parallel
To find the combined resistance of two resistors in parallel we use the
formula
R total = combined resistance value (ohms)
 R1 = value of resistance in first resistor (ohms)
 R2 = value of resistance in second resistor (ohms).
Alternatively you can use:

Example
Two resistors are combined in parallel. If they have values of 100
ohms and 1.2 kilo-ohms, determine the value of their combined
resistances. Note that the value of resistances have to be changed so
they are both either ohms or kilo-ohms. Ohms have to be used in this
example:
R total = R1 x R2/(R1 + R2)
so
R total = 100 x 1200/(100+1200) = 120000/1300 = 92 ohms
Time constant calculations
These are used to determine the time constant [time constant: in a
resistance/capacitance circuit, the time constant is the time taken to
charge the capacitor, through the resistor, to 63% of its full charge - or
to discharge it to 37% of its initial voltage. ] for a resistor and capacitor
in series. The time constant can be used to calculate time delays. The
formula is
T=CxR
 T = time constant (in seconds)
 C = value of capacitance (in farads)
 R = value of resistance (in ohms)
Example
A capacitor and a resistor are connected in series. Determine the time
constant for capacitance charging if the capacitor has a value of 100
micro-farads [micro-farads: units of capacitance equal to 1 millionth
of a farad ] and the resistor value is 100 kilo-ohms [kilo-ohms: units
of resistance equal to 1000 ohms ]>. Note that the capacitance has
been changed to whole farads (ie divided by 1,000,000) and the
resistance has been changed to ohms (ie multiplied by 1,000).
T = C x R = 100/1,000,000 x (100 x 1000) = 10 seconds
Transistor calculations
The formula for the relationship between currents in a transistor is
Ie = Ib + Ic
 Ie = emitter current (amps)
 Ib = base current (amps)
 Ic = collector current (amps)
Example
Determine the value of the emitter current (Ie) flowing through a
transistor if the base current = 0.015 amps and the collector current =
0.16 amps.
Ie = Ib + Ic = 0.015 + 0.16 = 0.175 amps
Current gain calculation
The formula for calculating a transistor's current gain [gain: the
amount of amplification of the input voltage - ie how much bigger the
output voltage is compared to the input voltage ] is
hFE = Ic/Ib
 hFE = current gain
 Ic = collector current (amps)
 Ib = base current (amps)
Example
A transistor has a current of 0.2 amps and 0.09 amps flowing through
the collector and the base respectively. Determine the value of the
current gain. Note that gain has no units because it is a ratio.
hFE = Ic/Ib = 0.2/0.09 = 2.2
Control circuit calculations
Potential divider circuit
You can calculate the value of the output voltage from a potential
divider using the formula:
Potential divider circuit
Vout = ( R2 /R1+R2 ) x Vin.
 Vout is the output voltage in volts
 R1 is the value of resistor R1 in ohms,
 R2 is value of resistor R2 in ohms.
 Vin is the input voltage in volts
Example
A potential divider has one resistor R1, with a resistance of 5 Ohms, a
resistor R2, with a resistance 10 Ohms and an input voltage of 5
Volts. What is the output voltage?
Vout = 10/(10+5) *5
Vout = 3.333
The table below gives examples of differrent potential divider
calcultations.
Vin
R1
R2
5 Volts
5 Ohms
10 Ohms 3.333 Volts
10 Volts 2 Ohms
3 Ohms
Vout
6 Volts
12 Volts 10 Ohms 12 Ohms 6.55 Volts
Operational amplifier gain
To find the gain of an inverting op-amp we use the formula
Gain = Rf/Rin
 Rf = value of feedback resistor (ohms)
 Rin = value of input resistor (ohms)
Example
An inverting op-amp has a 4.7 kilo-ohm feedback resistor and a 1 kiloohm input resistor. Determine the value of the amplifier gain.
Gain = - Rf/Rin = - 4.7/1.0 = - 4.7
(Nb: a gain is a ratio and so does not have any units)
Now try a Test Bite
Back to Revision Bite