Download Seven – Series and Parallel Circuits

Seven - Series and Parallel Circuits
1. state that Kirchoff's second law is = the sum of the e.m.f.'s around a loop is equal to the sum
of the p.d.'s around the same loop
- appreciate that this is due to the conservation of energy
2. define series circuit as a circuit in which the components are connected end-to-end and
therefore are in the same loop, so there is only one path for current to flow
- p.d. is shared between them whereas current is constant
3. define parallel circuit as a circuit in which there is more than one loop connected to the
power supply, therefore more than one path for current to flow
-current is always shared between loops whereas p.d. remains constant
𝑠𝑢𝑝𝑝𝑙𝑦 𝑒.𝑚.𝑓.
- 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑡𝑜𝑡𝑎𝑙 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
4. prove and use the equation for resistances in series circuit: RTOT = R1 + R2...
by applying KII:
VTOT = V1 + V2
by applying KI:
IRTOT = IR1 + IR2
cancel out I's because KI states that I
is constant in same loop:
RTOT = R1 + R2
also resistors in series means an increase in length of
resistors and R∝length, so increase in resistance
5. prove and use the equation for resistances in parallel circuits: 𝑅
1
𝑇𝑂𝑇
1
1
=𝑅 +𝑅 +⋯
1
2
by applying KI:
ITOT = I1 + I2
by applying KII:
VTOT = V1 = V2 V's get cancelled out from above equation
overall, cross-sectional-area of resistors
increase, and 𝑅 ∝
1
𝑐.𝑠.𝑎
, so resistance decreases
6. solve circuit problems involving series and parallel circuits with
more than one sources of e.m.f.
E1 > E2
I3 = I1 + I2
E1 = I3 x R1
E2 = (I3 x R1) + (I2 x R2)
7. explain that all sources of e.m.f. have an internal resistance:
- in battery due to chemicals
- in power supplies due to the components inside (e.g. wires)
8. select and use the equations:
- E = I (R + r) where R is the load resistance and r is the internal resistance and Ir is the "lost
volts"
- E = V + Ir
9. define terminal potential difference as the p.d. across the load (external) resistance
- terminal p.d. is the energy transferred when I coulomb of charge flows through the
external resistance
- V = E - Ir
10. describe the experiment used to show internal resistance:
set up circuit
set power pack to 10V
set resistance to low
record I and V
change R
record new I and V
repeat
plot V against I
compare to y = mx + c, y= V and x= I
m = -r and c = e.m.f.
11. explain maximum power dissipation in the external resistance occurs when both internal
and external resistances are equal, and when both resistances are equal for maximum
power, the efficiency is 50%
12. explain that maximum current is when the external resistance is zero (short circuited)
13. explain that maximum voltage is when the external resistance is 'infinite' and the efficiency
approaches 100%
14. explain that when the external resisitance is either zero, power dissipation in it is zero
When the external resistance is zero, the power dissipation in the internal resistance is
maximum (i.e. we have 0% efficiency)
15. understand that power that can be dissipated externally is calculated by:
𝑉𝑜𝑙𝑡𝑎𝑔𝑒𝐸𝑋𝑇𝐸𝑅𝑁𝐴𝐿
𝑃𝑜𝑤𝑒𝑟 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐸𝑋𝑇𝐸𝑅𝑁𝐴𝐿 × (
)2
(𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐸𝑋𝑇𝐸𝑅𝑁𝐴𝐿 + 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐼𝑁𝑇𝐸𝑅𝑁𝐴𝐿 )