128 CHAPTER 7. SYSTEMS OF EQUATIONS

10 volts

12 volts3 Ω

2 Ω

7 Ω

1 Ω

4 Ω

5 Ω 3 Ω

4 Ω2 Ω

I1 I2

I3

Those jagged places denote resistors and the numbers next to them give their resis-tance in ohms, written as Ω. The breaks in the lines having one short line and onelong line denote a voltage source which causes the current to flow in the directionwhich goes from the longer of the two lines toward the shorter along the unbrokenpart of the circuit. The current in amps in the four circuits is denoted by I1, I2, I3 andit is understood that the motion is in the counter clockwise direction. If Ik ends upbeing negative, then it just means the current flows in the clockwise direction. ThenKirchhoff’s law states that

The sum of the resistance times the amps in the counter clockwise direction arounda loop equals the sum of the voltage sources in the same direction around the loop.Find I1, I2, I3.

40. Here are some chemical reactions. Balance them.

(a) KNO3 +H2CO3→ K2CO3 +HNO3

(b) Ba3N2 +H2O→ Ba(OH)2 +NH3

(c) CaCl2 +Na3PO4→Ca3 (PO4)2 +NaCl

41. In the section on dimensionless variables 119 it was observed that ρV 2AB has theunits of force. Describe a systematic way to obtain such combinations of the vari-ables which will yield something which has the units of force.