Question

The ammeter in the figure below reads 1.0A. Calculate the magnitude of the currents I1 and I2.

Answer 1

We can see here that the magnitude of the currents are:

`I_(1)` = 0.5263 A

`I_(2)` = 0.2632 A

To calculate the currents,
`I_(1)` and
`I_(2)` in the circuit, we can use Ohm's law (V = IR) and the rules of series and parallel circuits.

Where we have:

`R_(1)` = 2.0 Ω

`R_(2)` = 4.0 Ω

`R_(3)` = 5.0 Ω

When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

We have:

`(1)/(R_(parallel) ) = (1)/(R_(1) ) +(1)/(R_(2)) +(1)/(R_(3) )`

= 1/2 + 1/4 + 1/5

= 0.5 + 0.25 + 0.2 = 0.95

`R_(parallel) = (1)/(0.95)` = 1.0526 Ω

In a series circuit, the total current passing through the circuit is the same at any point.

Given that the ammeter reads 1.0 A, this represents the total current passing through the circuit.

Using Ohm's law (V = IR) and the total resistance calculated (1.0526 Ω) along with the total current (1.0 A), we can find the total voltage across the entire circuit.

Total voltage (V) = Total current (I) × Total resistance (R)

Total voltage (V) = 1.0 A × 1.0526 Ω ≈ 1.0526 V

As the resistors are in parallel, the voltage across each resistor is the same as the total voltage (1.0526 V), and we can use Ohm's law to find the currents,
`I_(1)` and
`I_(2)` through
`R_(1)` and
`R_(2)`.

`I_(1)` = 1.0526 V/2.0 Ω = 0.5263 A

`I_(2)` = 1.0526 V/4.0 Ω = 0.2632 A

Answer 2

Given:

• Ammeter reading, I = 1.0 A

,

• R1 = 2.0 Ω

,

• R2 = 4.0 Ω

,

• R3 = 5.0 Ω

Let's find the magnitude of the currents in I1 and I2.

Apply Kirchhoff's Current Law.

We have:

`I_1+I_2+I_3=0`

From Kirchoff's junction rule:

`I_1-I_2-I_3=1A`

Thus, we have:

`\begin{gathered} (1)/(R_(eq))=(1)/(2)+(1)/(4)+(1)/(5) \\ \\ (1)/(R_(eq))=(10+5+4)/(20)=(19)/(20) \\ \\ R_(eq)=(20)/(19)=1.1\text{ ohms} \end{gathered}`

Apply Ohm's law to find the voltage in the circuit:

`\begin{gathered} V=IR \\ \\ V=1.0*1.1 \\ \\ V=1.1\text{ V} \end{gathered}`

To find I1, apply Kirchoff's loop law: