QuestionIn the figure, assume $R_{1}>R_{2}$ . (a) Is the potential difference across $R_{2}$ more than, less than, or equal to that across $R_{1}$ ? (b) Is the current through resistor $R_{2}$ more than, less than, or equal to that through resistor $R_{1}$ ?

Studdy Solution

STEP 1

What is this asking? We're checking out how voltage and current act in a circuit with parallel and series resistors!
Specifically, we're comparing the voltage and current across two parallel resistors, $R_1$ and $R_2$ , when $R_1$ is bigger than $R_2$ . Watch out! Don't mix up parallel and series connections!
Voltage is the same across parallel components, while current is the same through series components.

STEP 2

1. Voltage Comparison
2. Current Comparison

STEP 3

Alright, let's tackle the voltage first! $R_1$ and $R_2$ are connected in parallel, right?

STEP 4

And a key thing to remember about parallel connections is that the voltage across each component is the same!
It's like they're sharing the same electrical pressure.

STEP 5

So, even though $R_1 > R_2$ , the voltage across $R_1$ is equal to the voltage across $R_2$ .
Boom!

STEP 6

Now, let's dive into the current!
Ohm's Law is our trusty guide here: $V = I \cdot R$ , where $V$ is voltage, $I$ is current, and $R$ is resistance.

STEP 7

We just saw that the voltage across $R_1$ and $R_2$ is the same, let's call it $V$ .

STEP 8

For $R_1$ , we have $V = I_1 \cdot R_1$ , so $I_1 = \frac{V}{R_1}$ .

STEP 9

For $R_2$ , we have $V = I_2 \cdot R_2$ , so $I_2 = \frac{V}{R_2}$ .

STEP 10

We're given that $R_1 > R_2$ .
Since $R_1$ is in the denominator for $I_1$ , a larger $R_1$ means a smaller $I_1$ .
Similarly, since $R_2$ is in the denominator for $I_2$ , a smaller $R_2$ means a larger $I_2$ .

STEP 11

Therefore, the current through $R_2$ is more than the current through $R_1$ .
It's like the current finds it easier to flow through the path of less resistance!

STEP 12

(a) The potential difference (voltage) across $R_2$ is equal to that across $R_1$ . (b) The current through $R_2$ is more than that through $R_1$ .

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QuestionIn the figure, assume $R_{1}>R_{2}$ . (a) Is the potential difference across $R_{2}$ more than, less than, or equal to that across $R_{1}$ ? (b) Is the current through resistor $R_{2}$ more than, less than, or equal to that through resistor $R_{1}$ ?

Studdy Solution

STEP 1

STEP 2

1. Voltage Comparison
2. Current Comparison

STEP 3

Alright, let's tackle the voltage first! $R_1$ and $R_2$ are connected in parallel, right?

STEP 4

And a key thing to remember about parallel connections is that the voltage across each component is the same!
It's like they're sharing the same electrical pressure.

STEP 5

So, even though $R_1 > R_2$ , the voltage across $R_1$ is equal to the voltage across $R_2$ .
Boom!

STEP 6

Now, let's dive into the current!
Ohm's Law is our trusty guide here: $V = I \cdot R$ , where $V$ is voltage, $I$ is current, and $R$ is resistance.

STEP 7

We just saw that the voltage across $R_1$ and $R_2$ is the same, let's call it $V$ .

STEP 8

For $R_1$ , we have $V = I_1 \cdot R_1$ , so $I_1 = \frac{V}{R_1}$ .

STEP 9

For $R_2$ , we have $V = I_2 \cdot R_2$ , so $I_2 = \frac{V}{R_2}$ .

STEP 10

We're given that $R_1 > R_2$ .
Since $R_1$ is in the denominator for $I_1$ , a larger $R_1$ means a smaller $I_1$ .
Similarly, since $R_2$ is in the denominator for $I_2$ , a smaller $R_2$ means a larger $I_2$ .

STEP 11

Therefore, the current through $R_2$ is more than the current through $R_1$ .
It's like the current finds it easier to flow through the path of less resistance!

STEP 12

(a) The potential difference (voltage) across $R_2$ is equal to that across $R_1$ . (b) The current through $R_2$ is more than that through $R_1$ .

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QuestionIn the figure, assume R1>R2R_{1}>R_{2}R1​>R2​. (a) Is the potential difference across R2R_{2}R2​ more than, less than, or equal to that across R1R_{1}R1​ ? (b) Is the current through resistor R2R_{2}R2​ more than, less than, or equal to that through resistor R1R_{1}R1​ ?

Studdy Solution

STEP 1

STEP 2

1. Voltage Comparison2. Current Comparison

STEP 3

Alright, let's **tackle the voltage** first! R1R_1R1​ and R2R_2R2​ are connected in parallel, right?

STEP 4

And a key thing to remember about parallel connections is that the **voltage across each component is the same**!It's like they're sharing the same electrical pressure.

STEP 5

So, even though R1>R2R_1 > R_2R1​>R2​, the **voltage across** R1R_1R1​ **is equal to the voltage across** R2R_2R2​.Boom!

STEP 6

Now, let's **dive into the current**!Ohm's Law is our trusty guide here: V=I⋅RV = I \cdot RV=I⋅R, where VVV is voltage, III is current, and RRR is resistance.

STEP 7

We just saw that the **voltage across** R1R_1R1​ **and** R2R_2R2​ **is the same**, let's call it VVV.

STEP 8

For R1R_1R1​, we have V=I1⋅R1V = I_1 \cdot R_1V=I1​⋅R1​, so I1=VR1I_1 = \frac{V}{R_1}I1​=R1​V​.

STEP 9

For R2R_2R2​, we have V=I2⋅R2V = I_2 \cdot R_2V=I2​⋅R2​, so I2=VR2I_2 = \frac{V}{R_2}I2​=R2​V​.

STEP 10

We're given that R1>R2R_1 > R_2R1​>R2​.Since R1R_1R1​ is in the denominator for I1I_1I1​, a **larger** R1R_1R1​ means a **smaller** I1I_1I1​.Similarly, since R2R_2R2​ is in the denominator for I2I_2I2​, a **smaller** R2R_2R2​ means a **larger** I2I_2I2​.

STEP 11

Therefore, the **current through** R2R_2R2​ **is more than the current through** R1R_1R1​.It's like the current finds it easier to flow through the path of less resistance!

STEP 12

(a) The potential difference (voltage) across R2R_2R2​ is **equal to** that across R1R_1R1​. (b) The current through R2R_2R2​ is **more than** that through R1R_1R1​.

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QuestionIn the figure, assume $R_{1}>R_{2}$ . (a) Is the potential difference across $R_{2}$ more than, less than, or equal to that across $R_{1}$ ? (b) Is the current through resistor $R_{2}$ more than, less than, or equal to that through resistor $R_{1}$ ?

1. Voltage Comparison
2. Current Comparison

Alright, let's tackle the voltage first! $R_1$ and $R_2$ are connected in parallel, right?

And a key thing to remember about parallel connections is that the voltage across each component is the same!
It's like they're sharing the same electrical pressure.

So, even though $R_1 > R_2$ , the voltage across $R_1$ is equal to the voltage across $R_2$ .
Boom!

Now, let's dive into the current!
Ohm's Law is our trusty guide here: $V = I \cdot R$ , where $V$ is voltage, $I$ is current, and $R$ is resistance.

We just saw that the voltage across $R_1$ and $R_2$ is the same, let's call it $V$ .

For $R_1$ , we have $V = I_1 \cdot R_1$ , so $I_1 = \frac{V}{R_1}$ .

For $R_2$ , we have $V = I_2 \cdot R_2$ , so $I_2 = \frac{V}{R_2}$ .

We're given that $R_1 > R_2$ .
Since $R_1$ is in the denominator for $I_1$ , a larger $R_1$ means a smaller $I_1$ .
Similarly, since $R_2$ is in the denominator for $I_2$ , a smaller $R_2$ means a larger $I_2$ .

Therefore, the current through $R_2$ is more than the current through $R_1$ .
It's like the current finds it easier to flow through the path of less resistance!

(a) The potential difference (voltage) across $R_2$ is equal to that across $R_1$ . (b) The current through $R_2$ is more than that through $R_1$ .