3.5.1.4
P
Circuits & Potential Dividers — AQA A-Level Physics
- P.d. across each branch is the same in a parallelComponents connected across the same two points, providing multiple current paths. circuit.
- Total currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). from the supply equals the sum of branch currents.
- CurrentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). splits in inverse proportion to resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω)..
- The branch with the lowest resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). carries the most current.
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
- Total resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). in parallel is always less than the smallest individual resistor.
- Adding a resistor in parallel always decreases the total resistance.
- For two equal resistors R in parallel: $R_{\text{total}} = R / 2$.
Worked Example
A 30 ohm and a 60 ohm resistor are connected in parallel. Calculate the total resistance.
Show Solution
1
1/$R_{\text{total}} = 1/30 + 1/60$.
2
1/$R_{\text{total}} = 2/60 + 1/60 = 3/60$.
3
$R_total = 60/3 = 20 \;\Omega.$
Answer
20 ohm
Common Mistake
MEDIUM
Students often: Forgetting to take the reciprocal at the end: writing 1/R_total as the answer instead of R_total.
Instead: After summing 1/R_1 + 1/R_2, you must flip the result to get R_total. The final answer is never a fraction of 1/ohms.
Instead: After summing 1/R_1 + 1/R_2, you must flip the result to get R_total. The final answer is never a fraction of 1/ohms.
Examiner Tips and Tricks
- For two resistors in parallel, the 'product over sum' shortcut is faster: $R_{\text{total}} = (R_{1} x R_{2}) / (R_{1} + R_{2})$.
- Show working clearly.
Parallel resistor circuit
Two resistors R_1 and R_2 in parallel branches, with a cell and ammeterAn instrument that measures current. Connected in series with the component. Has very low resistance so it doesn't affect the circuit. in the main branch. I = I_1 + I_2 labelled.