## useful electronic formulae

**Ohms law.**

The voltage across a resistance is equal to the current passing through the resistance (in Amps) multiplied by the value of the resistance (in Ohms).

The voltage across a resistance is equal to the current passing through the resistance (in Amps) multiplied by the value of the resistance (in Ohms).

**Voltage = Current x Resistance or V=IR**

V=IR or I=V/R or R=V/I

V=IR or I=V/R or R=V/I

**Power.**

The power (in Watts) dissipated by a resistance is equal to the current (in Amps) passing through the resistance multiplied by the voltage (in Volts) across it.

The power (in Watts) dissipated by a resistance is equal to the current (in Amps) passing through the resistance multiplied by the voltage (in Volts) across it.

Power = Current x Voltage or P=IV

Using Ohms Law to substitute the voltage term we get:

Power = Current x Voltage or P=IV

Using Ohms Law to substitute the voltage term we get:

P = I x (IR) or P = I²R

Using Ohms Law to substitute the current term we get:

P = (V/R) x V or P = V²/R

As a practical example of this -

Q - Why would a person moving home from the UK to the USA be well advised to buy a new electric kettle?

P = I x (IR) or P = I²R

Using Ohms Law to substitute the current term we get:

P = (V/R) x V or P = V²/R

As a practical example of this -

Q - Why would a person moving home from the UK to the USA be well advised to buy a new electric kettle?

A - The kettle in the UK is rated at 2000 Watts on a voltage of 230V.

Applying the formula P = V²/R we can find the resistance of the kettle:

A - The kettle in the UK is rated at 2000 Watts on a voltage of 230V.

Applying the formula P = V²/R we can find the resistance of the kettle:

R = V²/P = 230²/2000 = 26.45 Ohms

R = V²/P = 230²/2000 = 26.45 Ohms

If the kettle were to be plugged into a 120V USA supply, its power would be:

If the kettle were to be plugged into a 120V USA supply, its power would be:

P = V²/R = 120²/26.45 = 544.4 Watts

P = V²/R = 120²/26.45 = 544.4 Watts

So, the kettle would produce around a quarter of the heat and would take roughly four times as long to boil.

If you halve the voltage, you get a quarter of the power.

So, the kettle would produce around a quarter of the heat and would take roughly four times as long to boil.

If you halve the voltage, you get a quarter of the power.

**Resistors in Series.**

The series connection is a "daisy-chain" arrangement - as shown

The series connection is a "daisy-chain" arrangement - as shown

**Rtotal = Ra + Rb**

So, if Ra was 10k (10,000 Ohms) and Rb was 22k (22,000 Ohms), their combined total resistance would be:

10,000 + 22,000 = 32,000 Ohms or 32k

It does not matter how many resistors are connected in series, their resistances are simply added together to get a total resistance

So, if Ra was 10k (10,000 Ohms) and Rb was 22k (22,000 Ohms), their combined total resistance would be:

10,000 + 22,000 = 32,000 Ohms or 32k

It does not matter how many resistors are connected in series, their resistances are simply added together to get a total resistance

**Resistors in Parallel**

In the parallel arrangement, the ends are connected together - as shown.

In the parallel arrangement, the ends are connected together - as shown.

**1/Rtotal = 1/Ra + 1/Rb**

**So, with Ra at 10k and Rb at 22k, the combined resistance Rtotal = 6.9k.**

Additional parallel resistors extend the formulae:

Additional parallel resistors extend the formulae:

**1/Rtotal = 1/Ra + 1/Rb + 1/Rc**

**Capacitors in Series**

The unit for capacitance is the Farad.

The unit for capacitance is the Farad.

**1/Ctotal = 1/Ca + 1/Cb**

**Capacitors in Parallel**

**Ctotal = Ca + Cb**

**Inductors in Series**

The unit for inductance is the Henry.

The unit for inductance is the Henry.

**Ltotal = La + Lb**

**Inductors in Parallel**

**1/Ltotal = 1/La + 1/Lb**

(c) Stephen Rand 2009 - 2017