3.Assess: Verify that the sum of the potential differences across series resistors matches that for the equivalent resistor. The sum of the currents through parallel resistors matches that for the equivalent resistor.
Series Elements.
A series connection has no junction. The current in each element is the same.
Resistors in a series can be reduced to an equivalent resistance:
R_{eq}=R_{1}+R_{2}+R_{3}+...
Capacitors in series can be reduced to:
an equivalent capacitance:
C_{eq}=(^{1}/C_{1}+^{1}/C_{2}+^{1}/C_{3}...)^{-1}
Parallel Elements are:
connected by wires at both ends.
The potential difference across each element is the same.
Resistors in parallel can be reduced to an equivalent resistance:
R_{eq}=(1/R_{1}+1/R_{2}+1/R_{3}...)^{-1}
Capacitors in parallel can be reduced to an equivalent capacitance:
C_{eq}=C_{1}+C_{2}+C_{3}+...
The time constant for decay is:
τ=RC
RC Circuits; the discharge of a capacitor through a resistor is an exponential decay:
ΔV_{C}=(ΔV_{C})_{ο}e^{-t/τ}
Electricity in the nervous system Cells in the nervous system maintain a negative potential inside the cell membrane.
When triggered, the membrane depolarizes and generates an action potential.
An action potential potential travels as a wave along the axon of a neuron. More rapid saltatory conduction can be achieved by:
insulating the axon with myelin, causing the action potential to jump from node to node.