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grandymaker [24]
3 years ago
9

Two resistors R1 = 6.7 Ω and R2 = 1.6 Ω are connected in parallel and a potential difference of ΔV = 12.0 V is imposed across th

em. Find the currents I1 and I2, and the current through the battery, I
Physics
1 answer:
Softa [21]3 years ago
6 0

Answer:

I1 = 1.8A

I2 = 7.5A

I = 9.3A

Explanation:

From the principle of basic electricity, when resistors are connected in parallel, the potential difference across them is the same but the current may vary depending on the value of the resistors.

Firstly we calculate the equivalent resistance in the circuit

1/R = 1/R1 + 1/R2

1/R = 1/6.7 + 1/1.6 = 0.774

R = 1/0.774 = 1.292Ω

Now let's calculate the total current flowing through the circuit (I)

V=IR

12=I × 1.292

I = 12/1.292 = 9.3A

The current flowing across R1 (I1) is calculated as

V = I1 × R1

12 = I1 × 6.7

I1 = 12/6.7

I1 = 1.8A

= 12/1.292 = 9.3A

The current flowing across R1 (I1) is calculated as

V = I1 × R1

12 = I1 × 6.7

I1 = 12/6.7

I1 = 1.8A

The current flowing across R2 is (I2) is calculated as

V = I2 × R2

12 = I2 × 1.6

I2 = 12/1.6

I2 = 7.5A

Confirming our overall current value

I1 + I2 = I

1.8A + 7.5A = 9.3A

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Taking into account the rule of three for the change of units, the mass of the book is 45600 miligrams.

First of all, the rule of three is a mathematical tool that helps you quickly solve proportionality problems.

Having three known values ​​and one unknown, a proportional relationship is established between all of them in order to find the fourth term of the proportion.

If the relationship between the magnitudes is direct (when one magnitude increases, so does the other; or when one magnitude decreases, so does the other), the rule of three is applied as follows, where a, b and c are known values ​​and x is the unknown to calculate:

a → b

c → x

So: x=\frac{cxb}{a}

Being 1 kg equivalent to 1000000 milligrams, In this case the rule of three is applied as follows: if 1 kg equals 1000000 milligrams, 4.56×10⁻² kg equals how many milligrams?

1 kg → 1000000 milligrams

4.56×10⁻² kg  → x

So:

x=\frac{4.56x10^{-2} kg x1000000 miligrams }{1 kg}

<u><em>x=45600 miligrams</em></u>

In summary, the mass of the book is 45600 miligrams.

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