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Ohm’s Law V = IR

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Example Problem A 4Ω, 8Ω and a 12Ω resistor are in series with a 24V battery. a. Calculate the equivalent resistance b. Calculate the current in the circuit c. What is the current in each resistor? d. What is the voltage drop across each resistor? 4Ω 24V 8Ω 12Ω

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**Calculate the equivalent resistance**

To get equivalent resistance (RT) in series, add all resistances in series. RT = 4Ω + 8Ω + 12Ω = 24 Ω 4Ω 8Ω 12Ω 24V 24Ω 24V

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**Calculate the current in the circuit**

To calculate the current, use V=IR 𝐼= 𝑉 𝑅 = 24𝑉 24Ω =1𝐴 24Ω 24V I = 1A

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**What is the current in each resistor? **

Since there are no branches to split the current, the current has to go through all of them. So the current is 1A 4Ω 8Ω 12Ω 24V I = 1A

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**What is the voltage drop across each resistor?**

To calculate the voltage drop, use V=IR 4Ω 8Ω 12Ω 24V V4Ω = (1A)(4Ω) = 4V V8Ω = (1A)(8Ω) = 8V V12Ω = (1A)(12Ω) = 12V I = 1A Notice how all the voltage drops add up to the voltage of the battery. 4V+8V+12V=24V

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**A 4Ω, 8Ω and a 12Ω resistor are in parallel with a 24V battery.**

a. Calculate the equivalent resistance b. Calculate the current in the circuit c. What is the current in each resistor? d. What is the voltage drop across each resistor? 24V 4Ω 8Ω 12Ω

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**𝑅 𝑇 = 24Ω 11 =𝟐.𝟐𝜴 24V 2.2Ω Calculate the equivalent resistance**

To get equivalent resistance in a parallel circuit, use the following equation: 1 𝑅 𝑇 = 1 𝑅 𝑅 𝑅 3 … 1 𝑅 𝑇 = 1 4Ω + 1 8Ω Ω = 6 24Ω Ω Ω = 11 24Ω 1 𝑅 𝑇 = 11 24Ω 𝑅 𝑇 = 24Ω 11 =𝟐.𝟐𝜴 Invert both sides 24V 2.2Ω

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**Calculate the current in the circuit**

To get the current in the circuit, use V=IR 𝐼= 24𝑉 2.2Ω =𝟏𝟎.𝟗𝐀 24V 2.2Ω I = 10.9A

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**𝐼 4Ω = 24𝑉 4Ω =𝟔𝐀 𝐼 8Ω = 24𝑉 8Ω =𝟑𝐀 𝐼 12Ω = 24𝑉 12Ω =𝟐𝐀 24V 4Ω 8Ω 12Ω**

What is the current in each resistor? To get the current in the circuit, use V=IR 𝐼 4Ω = 24𝑉 4Ω =𝟔𝐀 𝐼 8Ω = 24𝑉 8Ω =𝟑𝐀 𝐼 12Ω = 24𝑉 12Ω =𝟐𝐀 24V 4Ω 8Ω 12Ω

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**24V 4Ω 8Ω 12Ω What is the voltage drop across each resistor?**

What did we find in the lab about voltage in parallel? It’s the same! Voltage drop across each resistor is 24V 24V 4Ω 8Ω 12Ω

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