Download Electric Currents and more Schemes and Mind Maps Electrical Circuit Analysis in PDF only on Docsity!
Electric Circuits
Series Circuits
- A series circuit is a circuit in which there is only one pathway for the charges to travel through.
- Because there is only one pathway for the flow of electricity in a series circuit, the current measured at any point in the circuit will be the same.
R 1 R 2
=> Itot = I 1 = I 2 = · · · = In
- The total resistance of the individual resistors(like bulbs) in series is equivalent to using one resistor => Rtot = R 1 + R 2 + · · · + Rn
- The potential difference across the terminals of the battery(voltage source) is equal to the sum of all the potential differences or ‘voltage drop’ across the components
=> Vtot = V 1 + V 2 + · · · + Vn
Q1) Three resistors, with resistances of R 1 =2Ω, R 2 =4Ω and R 3 =6Ω are connected in a series to a 3V battery. Find the equivalent resistance(=total resistance) and the current in the circuit.
R 1 R 2 R 3
Q 2 ) A R 1 =4Ω and a R 2 =6Ω resistor are connected in a series with a 3V battery. Find the voltage across each resistor.
R 1 R 2
Parallel Circuits
- In a parallel circuit there is more than one pathway for the electric current to travel. If the individual resistors in our circuit each provide different resistances, there would be different amounts of current flowing through each path.
=> Itot = I 1 + I 2 + · · · + In
- Because the potential difference across each resistor is the same as the potential difference supplied by the battery
=> Vtot = V 1 = V 2 = · · · = Vn
R 1 R 2
V
- The total resistance in a parallel circuit will always be lower than any of the individual resistances. That is, two parallel resistors behave as a single resistance smaller than either one of them
=> 𝟏 𝑹𝒕𝒐𝒕
𝟏 𝑹𝟏
𝟏 𝑹𝟐
𝟏 𝑹𝒏
Q 3 ) A R 1 =3Ω resistor is connected in parallel to a R 2 =5Ω resistor. What is the total resistance? If circuit is connected to 9V battery, what is the current through each resistor?
R 1 R 2
V=9V
Electric Power The rate at which electrical energy is converted into another form such as mechanical energy, heat, or light is called electric power. For example, how much work a machine performs per rate is represents the power done by the machine.
Work = Power / time
Using W=Fd = qEd, V=Ed, I=q/t and I=V/R, we can derive
P = IV = I^2 R =
𝑽𝟐 𝑹 =^
𝑾 𝒕
Electric power(P) = Current(I) × voltage(V)
where the unit for power is [Watt]
Series Circuit Parallel Circuit I = V / R : Ohm’s law Itot = I 1 = I 2 = · · · = In Itot = I 1 + I 2 + · · · + In Vtot = V 1 + V 2 + · · · + Vn Vtot = V 1 = V 2 = · · · = Vn Power P=W/t = IV = I 2 R = V 2 /R (^) Rtot = R 1 + R 2 + · · · + Rn^1 𝑅𝑡𝑜𝑡^ =^
1 𝑅 1 +^
1 𝑅 2 + · · · +^
1 𝑅𝑛
Q8) Three resistors, R 1 =5Ω, R 2 =8Ω and R 3 =12Ω are connected in a parallel circuit with a 9V battery. Find the total resistance, the total current, the current through each resistor, the voltage across each resistor, and the power converted by each resistor
R 1 R 2
R 3
9V
