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elena-14-01-66 [18.8K]

3 years ago

9

For the electric circuit given below, calculate: 3 (i) the equivalent resistance of the circuit, (ii) the total current drawn fr

om the battery and (iii) the voltage across 7Ω resistor.

1 answer:

Daniel [21]3 years ago

3 0

Answer:

1)31/3Ω

2)18/31A

3)4.06V

Explanation:

According to the diagram and 10 Ω resistors are parallel to each other, parallel resistor can be calculated using the formula below

1/R= 1/R1 + 1/R2

But we know R1= 5 Ω and R2= 10 Ω

1/R= 1/5 + 1/10

R= 10/3 Ω

=3.33 Ω

Then if we follow the given figure, 10/3 Ω and 7Ω are now in series then

Req = 10/3 +7

Req= 31/3 Ω

Therefore, equivalent resistance = 31/3 Ω

According to ohms law we know that V= IR

Then I= V/R

Where I= current

R= resistance

V= voltage

I= 6/(31/3)

I= 18/31A

We can now calculate the voltage accross the resistor which is

V=(18/31)× 7

V=4.06V

Therefore, the voltage accross the 7 ohm resistor is 4.06V

CHECK THE FIQURE AT THE ATTACHMENT

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What force (in N) must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2100 kg car (a large car

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Complete Question:

What force (in N) must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2100 kg car (a large car) resting on the slave cylinder ? The master cylinder has a 2.00-cm diameter and the slave has a 24.0-cm diameter

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Given

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$D_2 = 24.0\ cm$ --- diameter of the slave cylinder

To do this, we apply Archimedes' principle of buoyancy which implies that:

$P = \frac{F_1}{A_1} = \frac{F_2}{A_2}$

Where

<em /> $F_1 = Force\ on\ the\ master\ cylinder$ <em />

<em /> $F_2 = Force\ on\ the\ slave\ cylinder$ <em />

<em /> $A_1 = Area\ of\ the\ master\ cylinder$ <em />

<em /> $F_2 = Area\ of\ the\ small\ cylinder$ <em />

<em />

Calculating the area of the master cylinder.

$A_1 = \pi r_1^2$

$r_1 = \frac{1}{2}D_1 = \frac{1}{2} * 2.00cm = 1.00cm$

$A_1 = \pi* 1^2$

$A_1 = \pi * 1$

$A_1 = \pi$

Calculating the area of the slave cylinder.

$A_2 = \pi r_2^2$

$r_2 = \frac{1}{2}D_2 = \frac{1}{2} * 24.00cm = 12.00cm$

$A_2 = \pi* 12^2$

$A_2 = \pi* 144$

$A_2 = 144\pi$

Substitute these values in:

$P = \frac{F_1}{A_1} = \frac{F_2}{A_2}$

$\frac{F_1}{\pi} = \frac{F_2}{144\pi}$

Multiply both sides by $\pi$

$\pi * \frac{F_1}{\pi} = \frac{F_2}{144\pi} * \pi$

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The force exerted on the slave cylinder (F2) is calculated as:

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$F_2 = 2100 * 9.8$

$F_2 = 20580$

Substitute 20580 for F2 in $F_1 = \frac{F_2}{144}$

$F_1 = \frac{20580}{144}$

$F_1 = 142.92N$

<em>Hence, the force exerted on the master cylinder is approximately 142.92N</em>

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