1. Voltage V as a function of time (V(t)) is equal to injected current I multiplied by R (which is the resistance) multiplied by 1 minus "e" (exponent) in the power of minus "t" (time) divided by R multiplied by C.
2. Let's check the equation by assuming the time (t) is indeed zero (meaning that we're at the "initial condition" (the "resting state", see below). So if t=o, then "e" to the power of zero is 1, 1 minus 1 is zero, so V(t=0)=0. This means that our "initial condition" (t=0) is satisfied.
3. Now let's look at the other extreme which is the case where time (t) equals infinity (∞), meaning that I inject my current for a very long time. So if (t) goes to infinity then "e" to the power of (t) goes to zero, then 1 minus zero is 1 and finally you're left with V(t=∞)=I.R which means that the cell/circuit enters the "steady state" (check the capacitors theory video above for explanation of the steady state, --ok, don't scroll up, just click here) or better, the voltage remains at its steady state.
That was all! Keep it up, beginner neuroscientist, you!
(source: khanacademy, brightstorm @ YouTube)
1. Ohm’ s Law: Current through a circuit is proportional to voltage (I=V/R). V is calculated with volts, R with Ω (ohms) and I with A (amperes, which in turn equal to C/S (=coulomb/second)). We could also say that V=I.R. A circuit is a “bunch” of wires that connect a set of circuit elements.
2. Current is the flow of charge per second, or the change of charge (ΔQ) to change of time (sec. or Δt).
3. The resistor determines the rate with which the electrons travel through the entire circuit (or all electrons travel with the same speed in a given circuit). The resistor serves as a “bottleneck” which regulates the speed of current. Resistors use energy.
4. In traditional/conventional schematics, the current flows from positive to negative pole in a circuit but this is wrong. In reality, it flows the other way.
5. The amount of voltage (or potential difference) in a circuit determines the “urge” or the “speed” with which the electrons (negative pole) want to travel and get to the positive pole.
6. Voltage is not an absolute number. It is a calculated number, it’s the potential difference between two points in a circuit and this number is always constant.
7. Resistors in series increase the probability of an electron “bump” onto something so it decelerates (and creates heat). The total resistance in such a circuit equals to the sum of each resistor. So resistors in series increase the total resistance of a circuit (example: Christmas lights, in goes out, all go out). Also in resistor in-series, the current (I ) is the same.
8. Resistors in parallel create “branches” within the circuit. The current (Amperes) through each branch is proportional to the resistance in Ω’s of each resistor. To find the total resistance (equivalent resistance) between resistors in parallel equals to: 1/Rt=1/R1+1/R2+1/Rn. So resistors in parallel reduce the overall resistance and the smallest current flows through the largest resistor (since it creates bigger resistance so less current can flow through it). So the effective resistance (or total resistance of a circuit) of resistors in parallel is always smaller than any of the resistors in parallel (example: house wiring, all electrical devices are separate parallel branches of the same circuit, since once doesn’t want to turn the TV in order to turn on the oven). In resistors in-parallel the voltage (or potential difference – V) is the same.
9. A circuit is a “bunch” of wires that connect a set of circuit elements.
10. Power (wattage) equals to amperes (current) times volt (voltage), (P=I.V) and is the rate of energy use. P also equals to V2/R since I=V/R or I2.R since V=I.R.