This document discusses several key concepts related to electromotive force (EMF) and potential divider circuits: 1. A potential divider circuit uses two resistors (R1 and R2) connected in series to a power supply. The voltage is divided between the two resistors based on their relative resistances. 2. If R1 = R2, then the voltage measured at each resistor (V1 and V2) will be half the supply voltage. As R2 increases relative to R1, V2 increases and V1 decreases. 3. The total voltage measured across R1 and R2 must equal the supply voltage, so V1 + V2 = Vin. This relationship allows the divided

1. EMF: Electromotive force (E)
Potential Divider Circuits
Current I = ∆Q Charge (c) E = V2 x t Power (P) - Energy
J/s - watt
Amps (A) transferred per unit of
∆t Time (s) time.
R1 V1
P = ∆E
For electricity
5V DC
P=
Vin
Any System
Current = rate of flow of charge -electrons in a wire
-electrons in beam
R2 V2 ∆t
P = V2
or...
-ions (beam/solution)
NB:∆ = small change in
P = IV
R
If R1 = R2 then V1 reads 2.5V
N=I = charge/sec E = ItV V2 reads 2.5V
Making good sensors
q As R2 increases then V2 increases & V1
• High resolution -the smallest change the sensor can
No. of ions/ sec decreases
detect. Precision of a sensor depends upon resolution.
V1 + V2 ≡ 5V
2 Chapter 2 • Appropriate output for a given input (Sensitivity) -ratio
E = I RT of change of output to change of input. (Eg Oscilloscope
Sensing R1 = V1
mm/volt)
• Rapid response time –time taken to respond to a
Potential Difference - difference in energy per R2 v2
change in input.
coulomb between two places in a circuit V2 = R2__ • Small unsystematic fluctuations (random error) in results
Vin R1 + R2 (Noise, random error, fluctuations) -present in all
V = ∆E Energy transferred (J)
experiments, the size limits the precision of measurements.
∆Q Averages improve the final results.
Energy flowing (c) • Small systematic error –very hard to detect, include zero error
and error due to disturbing influences. ‘Smart’ systems process
Rinternal
Rinternal
Output
information to compensate for disturbing influences.
Rexternal
EMF (E)
No. of charge Drift Source : Some Ohm’s Law –resistance and conductance
P.d. J/c or Volts (V) carriers resistance • The conductance or resistance can be
I= E_______ calculated at any given p.d.
I = nAvq Rexternal + Rinternal • If the conductance or resistance are
Output constant, independent of the current
G=I V = I x Rexternal or p.d., the conductor is said to obey
V = IR
3
Area (m ) Charge
V = E - I x Rinternal Ohm’s law, or to be ‘ohmic’.
• Ohm's law thus says that the
Source: High Source: Low conductance, and resistance, of a
G=G1+G2+G3…
A1 resistance resistance given component is constant. The
R=1 R1
Rinternal ≈ ∞ Rinternal ≈ 0 same value can be used in calculations
G
R=V V R1 R2 R2 I≈0
Output
I= E_______
Rexternal + Rinternal •
what ever the current or p.d.
Most metals are ohmic at constant
R=R1+R2+R3… V
I A1 A2 G=1 A1
R2
V = I x Rexternal ≈ 0 Output temp.; ionised gases are not.
A1+A2
R
A1 V = I x Rexternal ≈ E See also Chapter 4