1.11 - Internal resistance, series and parallel
circuits, and the potential divider
Conservation of energy in circuits
● “Energy cannot be created or destroyed, it can only be converted from one form to
another”
● ∵ E=QV , ∴ Q ×ε ( EMF)=Q V 1 +QV 2+Q V 3 +.. ., ε =V 1 +V 2 +V 3+ ...
● ∵ V =IR , ∴ ε =I R1 + I R 2+ I R 3+ ..., *** Σ ε (circuit EMF )=Σ IR
● In a common cell, V0 ≠ ε (ie there will always be some internal resistance)
Internal resistance
● NOT all chemical energy of cell is converted to electrical energy for the circuit
●
2 2
ε I (rate of energy converted∈cell ; power )=I r (rate of work done against internalresistance)+ I R (rate o
ε (EMF [V ])=I ×r (internal resistance [Ω])+ I × R(circuit resistance [Ω])
V (PD [V ])=ε −Ir
○ Rearrange equation into y = mx + c form, ***V =−rI +ε (as internal resistance
ALWAYS remains constant [at least in short period of time], & depends on the
type of cell)
● As the age of a cell increases, its r increases until it cannot generate any EMF (ie
chemical energy of cell has been used up)
Solar cells (photovoltaic)
● When light strikes the photocell, it gives some of its energy to free electrons in the
semiconductor material of the cell (commonly silicon)
● An electric field within the cell provides a force on the electrons
● Electron flow then provides current, the cell’s electric field causes voltage
simultaneously
● With both current & voltage, we have power
Principle of potential dividers (voltage dividers)
● Purposes:
1. Provide a variable PD
2. Enable a specific PD to be chosen
3. Split PD + resistance of a single power source between ≥2
components
● Common industrial/domestic uses:
1. Volume controls
2. Sensory circuits (LDRs, thermistors)
1
circuits, and the potential divider
Conservation of energy in circuits
● “Energy cannot be created or destroyed, it can only be converted from one form to
another”
● ∵ E=QV , ∴ Q ×ε ( EMF)=Q V 1 +QV 2+Q V 3 +.. ., ε =V 1 +V 2 +V 3+ ...
● ∵ V =IR , ∴ ε =I R1 + I R 2+ I R 3+ ..., *** Σ ε (circuit EMF )=Σ IR
● In a common cell, V0 ≠ ε (ie there will always be some internal resistance)
Internal resistance
● NOT all chemical energy of cell is converted to electrical energy for the circuit
●
2 2
ε I (rate of energy converted∈cell ; power )=I r (rate of work done against internalresistance)+ I R (rate o
ε (EMF [V ])=I ×r (internal resistance [Ω])+ I × R(circuit resistance [Ω])
V (PD [V ])=ε −Ir
○ Rearrange equation into y = mx + c form, ***V =−rI +ε (as internal resistance
ALWAYS remains constant [at least in short period of time], & depends on the
type of cell)
● As the age of a cell increases, its r increases until it cannot generate any EMF (ie
chemical energy of cell has been used up)
Solar cells (photovoltaic)
● When light strikes the photocell, it gives some of its energy to free electrons in the
semiconductor material of the cell (commonly silicon)
● An electric field within the cell provides a force on the electrons
● Electron flow then provides current, the cell’s electric field causes voltage
simultaneously
● With both current & voltage, we have power
Principle of potential dividers (voltage dividers)
● Purposes:
1. Provide a variable PD
2. Enable a specific PD to be chosen
3. Split PD + resistance of a single power source between ≥2
components
● Common industrial/domestic uses:
1. Volume controls
2. Sensory circuits (LDRs, thermistors)
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