1.1 Voltage

A storage battery has a charging profile as shown in Figure 1.1. After 300 seconds a total charge of fifty coulombs is transferred to the battery. Determine the battery voltage, assuming it was completely discharged.

Figure 1.1: Battery charging profile

Solution:

Q = 50 coulombs

V = J/Q volts

W = J/t watts

The charging profile can be expressed as

y = mx + b

where m = ? 0.01, b = 3, and x = t

W = ?0.01t + 3 watts

J = [ ?0.005 t ² + 3 t] ³⁰⁰ ₀ = 450 joules

V = J/Q = 450/50 = 9 volts

1.2 Current

A storage battery has five coulombs of charge remaining. It is recharged at a uniform rate for 300 seconds as shown in Figure 1.2. Determine the charging current.

Figure 1.2: Battery recharge rate

Solution:

I = Q/t amperes

The recharge rate can be expressed as

y = mx + b

where m = 0.15, b = 5, and x = t

Q = 0.15t + 5 coulombs

I = 0.15 amperes

1.3 Resistance

A cylindrical copper pipe section has an outside diameter of 1.0 cm and a wall thickness of 0.025 cm. Its overall length is 250 cm as shown in Figure 1.3. Determine its resistance assuming the resistivity constant, ?, equals 1.72 10 ^?6 ohms-cm.

Figure 1.3: Copper pipe section

Solution:

where r = D / 2, b =...