A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300kcal/kg⋅°C , assuming no heat escapes?

(a) the battery’s internal resistance is 0.4 Ω

(b) the dissipated power dissipated inside the battery is 40 W

(c) the  rate 0.096°C/min

Explanation:

Given information:

emf, ε = 12 V

voltage, V = 16 V

current, I = 10 A

mass, m = 20 kg

specific heat, c = 0.300 kcal/kg°C = 1255.8 J/kg°C

(a) What is the battery’s internal resistance?

to calculate the internal resistance, we can calculate by using the following formula

V = ε - Ir

where

V = voltage (V)

I = current (A)

r = internal resistance (Ω)

ε = emf (V)

since the battery is being charged, the current is negative, so

V = ε - (-I) r

V = ε + Ir

r = (V- ε)/I

 = (16 - 12)/10

 = 0.4 Ω

(b) What power is dissipated inside the battery?

to determine the dissipated power in the battery, use the following equation

P = I²r

where

P = power (W)

P = (10)² (0.4)

  = 40 W

(c) At what rate (in °C/min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300kcal/kg⋅°C , assuming no heat escapes

to find the rate of temperature increase by

Q = m c ΔT

where

Q = thermal energy (J)

c = specific heat (J/kg°C)

ΔT = the change of temperature

to find the energy, we use

E = Pt

the energy is converted in one minute

E = 40 x 60

  = 2400 J

thus,

2400 = 20 x 1255.8 x ΔT

ΔT = 2400/(20 x 1255.8)

     = 0.096°C/min

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

answera compound;