8.1.1
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The rate at which (electrical) energy is converted (to other forms) (in a circuit).![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Or
The rate at which energy is used/energy used per second. ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Or
The rate at which work is done.![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Tip: the amount of work done or energy transferred per unit of time has to be clear.
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2 marks
(1 x 2 marks)
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8.1.2
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Option 1
![P=\frac{V^2}{R}](https://studyclixsazalive.blob.core.windows.net/cms/media/d620101e-30f8-4e78-83aa-c933ee2e85ac.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![6=\frac{(12)^2}{R}](https://studyclixsazalive.blob.core.windows.net/cms/media/89646a4e-3ef0-4066-a543-0b5e86638570.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![\mathrm{R}=24\Omega](https://studyclixsazalive.blob.core.windows.net/cms/media/ab58473c-d6be-4984-96de-9db67ed9df86.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Tips:
- The most direct method to calculate the resistance is to use the power of 6W and the potential difference of 12V as shown above.
- Other methods can be used to get to the correct answer.
There are more ways to answer this question. To view other options, click here.
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3 marks
(3 x 1 mark)
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8.1.3
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How to approach this question:
- The first step is to calculate the effective resistance of the parallel resistors using the values calculated in question 8.1.2.
Option 1
Part 1
![\frac{1}{R_{//}}=\frac{1}{R_1}+\frac{1}{R_2}](https://studyclixsazalive.blob.core.windows.net/cms/media/ee2fc7da-d634-4c40-851c-8f40c87676cc.svg)
![=\frac{1}{24}+\frac{1}{24}](https://studyclixsazalive.blob.core.windows.net/cms/media/1dcdcf77-23df-4091-b38a-a1e16fac37c0.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![\mathrm{R}_{//}=12\Omega](https://studyclixsazalive.blob.core.windows.net/cms/media/baaf9e2b-7336-4eea-8cea-1fc87633da82.svg)
- The total resistance is the sum of the parallel resistors B and C as well as the resistor A.
![R_{ext}=\left(R_{s}+R_{//}\right)](https://studyclixsazalive.blob.core.windows.net/cms/media/6d8c317f-cca8-488c-b0fc-efb0800180b6.svg)
![R_{ext}=(24+12)](https://studyclixsazalive.blob.core.windows.net/cms/media/2e0287ea-d5be-4a2e-83e3-fb9a5a48dfd9.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=36\Omega](https://studyclixsazalive.blob.core.windows.net/cms/media/8fec7242-c71b-4bc2-a7b4-0d18561a1334.svg)
![](https://studyclixsazalive.blob.core.windows.net/cms/media/03c8a53d-5dc2-4238-8c58-4c5458c27be4.png)
Or
![R_{\text{total }}=\left(R_{s}+\frac{R_1R_2}{R_1+R_2}\right)](https://studyclixsazalive.blob.core.windows.net/cms/media/db381857-340a-42d8-89ab-ae6f608c79db.svg)
![R_{\text{total }}=\left\{24+\frac{(24)(24)}{48}\right\}](https://studyclixsazalive.blob.core.windows.net/cms/media/3d8e472e-483d-45a8-8e7e-8a5cfe2f7627.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=36\Omega](https://studyclixsazalive.blob.core.windows.net/cms/media/a54e8f5c-1608-44de-9300-dee3df45ab3a.svg)
Part 2
- The current can be calculated using the emf of 12V, the external resistance of 36 Ω and the internal resistance of 2Ω.
![V=IR](https://studyclixsazalive.blob.core.windows.net/cms/media/fd62432a-8803-4c50-b18f-1ea76997c51e.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Or
![\varepsilon=l(R+r)](https://studyclixsazalive.blob.core.windows.net/cms/media/17e467c3-3c92-446f-90be-d2867a17f497.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![12=I(36+2)](https://studyclixsazalive.blob.core.windows.net/cms/media/9310d808-3809-42db-ae3e-cc58ccef0858.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![I=0,32A(0,316A)](https://studyclixsazalive.blob.core.windows.net/cms/media/04c9eaf9-d9c0-49a4-9964-995f43f4954c.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
There are more ways to answer this question. To view other options, click here.
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5 marks
(5 x 1 mark)
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8.1.4
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Option 1
![V=IR](https://studyclixsazalive.blob.core.windows.net/cms/media/4d98fd0a-29ff-4d2c-aaa2-16e4b1057c8d.svg)
![\mathrm{V}=\mathrm{I}\left(\mathrm{R}_{\mathrm{A}}+\mathrm{r}\right)](https://studyclixsazalive.blob.core.windows.net/cms/media/0a0c00d0-8213-4149-a53d-e70e84e04ee4.svg)
![=0,316(26)](https://studyclixsazalive.blob.core.windows.net/cms/media/582d467c-de89-4800-b909-e2aa48df8898.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=8,216\vee(8,32\vee)](https://studyclixsazalive.blob.core.windows.net/cms/media/f5c8763a-17c9-48c8-a054-5b4be0c1bf10.svg)
![V_{//}=(12-8,216)](https://studyclixsazalive.blob.core.windows.net/cms/media/08ffe63e-2fee-4e98-8d16-8fdcd4952321.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=3,784\mathrm{~V}(3,68\mathrm{~V})](https://studyclixsazalive.blob.core.windows.net/cms/media/80ce737b-5273-4534-a8af-739bc5302cf0.svg)
![\therefore\mathrm{V}_{\mathrm{C}}=3,78\mathrm{~V}(3,68\mathrm{~V})](https://studyclixsazalive.blob.core.windows.net/cms/media/542b6930-fa69-46f6-aabd-0aac6fbe17f0.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Or
Option 2
![V=IR](https://studyclixsazalive.blob.core.windows.net/cms/media/90d21c2d-8341-4d74-b667-8e84405c7611.svg)
For the parallel portion:
![\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\text{ OR }R=\frac{R_1R_2}{\left(R_1+R_2\right)}](https://studyclixsazalive.blob.core.windows.net/cms/media/51b1cc44-7fdf-4857-aa75-d80d4ddbe323.svg)
![R=\frac{(24)(24)}{48}](https://studyclixsazalive.blob.core.windows.net/cms/media/25b5fa1d-ceb9-4496-8528-1e255a3c556d.svg)
![=12\Omega](https://studyclixsazalive.blob.core.windows.net/cms/media/ba204afa-896f-46b2-b87d-3772d17ccaaa.svg)
![V_{//}=V_{C}](https://studyclixsazalive.blob.core.windows.net/cms/media/5087a601-b713-438c-8591-cbcdacd6e12c.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![V=IR_{//}](https://studyclixsazalive.blob.core.windows.net/cms/media/b6a74f9b-9c68-46ed-8359-0183aaeb8d44.svg)
![=(0,316)(12)](https://studyclixsazalive.blob.core.windows.net/cms/media/caf9d484-1200-47c1-bafc-db12cff36283.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=3.79\mathrm{~V}(3,84\mathrm{~V})](https://studyclixsazalive.blob.core.windows.net/cms/media/323f6823-e9cc-496e-b8cf-2e6c05e562a7.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Or
Option 3
![I_{A}=I_{B}+I_{C}](https://studyclixsazalive.blob.core.windows.net/cms/media/f78bd286-2608-45e4-8410-50575fbd2a9f.svg)
![=2\mathrm{I}_{\mathrm{B}}](https://studyclixsazalive.blob.core.windows.net/cms/media/68e0f181-222c-49f3-8582-6a74a5a984ef.svg)
![0,316=2\mathrm{I}_{\mathrm{B}}](https://studyclixsazalive.blob.core.windows.net/cms/media/0847ff86-9a07-4f04-9133-d78aefb81ab5.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![\mathrm{I}_{\mathrm{B}}=0,158\mathrm{~A}](https://studyclixsazalive.blob.core.windows.net/cms/media/443f07ed-f491-463d-a396-b4c6fa3db46f.svg)
![V=0.158(24)](https://studyclixsazalive.blob.core.windows.net/cms/media/2b365edb-17e7-48ec-bfdb-089d3bc5c805.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
![=3,79\mathrm{~V}](https://studyclixsazalive.blob.core.windows.net/cms/media/7f65b39d-c379-4e14-8576-340b663934d7.svg) ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Tip: the potential difference across the parallel components can be determined by subtracting the product of the current and the sum of the resistance of A as well as the internal resistance from the emf.
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3 marks
(3 x 1 mark)
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8.1.5
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Option 1
- The power rating (output voltage) of the bulb is 6 W, 12 V.
![\mathrm{P}=\frac{V^2}{R}](https://studyclixsazalive.blob.core.windows.net/cms/media/dbd120e1-8955-4dd4-abaf-2e6206575987.svg)
- For a given resistance, power is directly proportional to V2.
- Since the potential difference across light bulb C calculated in question 8.1.5 is less than the operating voltage of 12V,
the output/power will be less. ![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
There are more ways to answer this question. To view other options, click here.
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3 marks
(3 x 1 mark)
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8.2.1
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The total current passes through resistor A. For the parallel portion, the current branches, therefore, only a portion of the total current passes through resistor C.![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
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2 marks
(2 x 1 mark)
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8.2.2
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The current in B is equal to the current in A. The circuit becomes a series circuit.![check](https://studyclixsazalive.blob.core.windows.net/cms/media/binl1ryy/tick-green-circle.svg)
Tips:
- The current is the same at all points in a series circuit.
- When resistor C is removed, resistors A, B and D are all connected in series.
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2 marks
(2 x 1 mark)
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