MS. Законы Кирхгофа (1)

 1   A                                                                                                                                          [1]

 2   B                                                                                                                                           [1]

 3   B                                                                                                                                           [1]

 4   B                                                                                                                                           [1]

 5   B                                                                                                                                           [1]

 6   The sum of the currents into a point = sum of currents out of the same point.                             [1]

 7   a    I = 2.0 + 1.0 = 3.0 A                                                                                                          [1]

b    0.7 + 0.5 = I therefore I = 1.2 A                                                                                    [1]

c    2.0 + I = 4.0 + 0.5                                                                                                             [1]

I = 4.5 - 2.0 = 2.5 A                                                                                                          [1]

 8   a    E = 1.5 + 1.5 = 3.0 V                                                                                                         [1]

b    E = 1.5 + 1.5 + 1.5 - 1.5 = 3.0 V                                                                                        [1]

c    E = 1.5 - 1.5 = 0 V                                                                                                           [1]

 9   ∑ e.m.f.= ∑ p.d.                                                                                                                     [1]

6.0 = (I ´ 10) + (I ´ 20) (clockwise ‘loop’)                                                                            [1]

30I = 6.0 so  I =  = 0.20 A                                                                                           [1]

10  a    ∑ e.m.f. = ∑ p.d.

6.0 - 1.5 = (I ´ 68) + (I ´ 12) (clockwise ‘loop’)                                                              [1]

80I = 4.5                                                                                                                          [1]

so I =                                                           [1]

b    V = IR = 5.63 ´ 10⁻² ´ 68 (the current is the same in a series circuit)                                 [1]

                                                                                                                        [1]

c     The resistance of the voltmeter is infinite (or very large).                                                    [1]

11  Loop 1:   ∑ e.m.f. = ∑ p.d.

          3.0 = 10I₁ + 20I₂     (equation 1)                                                                              [1]

Loop 2:   ∑ e.m.f. = ∑ p.d.

          1.5 = 20I₂               (equation 2)                                                                              [1]

          I₂ =  = 0.075 A                                                                                                  [1]

Substituting the value for I₂ into equation 1, we have:

3.0 = 10I₁ + (20 ´ 0.075)                                                                                                         [1]

I₁ = = 0.15 A                                                                                                                    [1]

Finally, using Kirchhoff’s first law, we have:

0.15 = 0.075 + I₃

I₃ = 0.075 A                                                                                                                           [1]