The exponent of the exponential function contains RC for the given circuit, which is called the time constant. Use the units of R and C to find units of RC. Write ohms in terms of volts and amps and write farads in terms of volts and coulombs. Simplify until you get something simple. Show your work below.

The unit of the time constant RC is the second

Explanation:

The unit of resistance, R is the Ohm, Ω and resistance, R = V/I where V = voltage and I = current. The unit of voltage is the volt, V while the unit of current is the ampere. A.

Since R = V/I

Unit of R = unit of V/unit of I

Unit of R = V/A

Ω = V/A

Also, The unit of capacitance, C is the Farad, F and capacitance, F = Q/V where Q = charge and V = voltage. the unit of charge is the coulomb, C while the unit of voltage is the volt, V

Since C = Q/V

Unit of C = unit of Q/unit of V

Unit of C = C/V

F = C/V

Now the time constant equals RC.

So, the unit of the time constant = unit of R × unit of C = Ω × F = V/A × C/V = C/A

Also. we know that the  1 Ampere = 1 Coulomb per second

1 A = 1 C/s

So, substituting 1 A in the denominator, we have

unit of RC =  C/A = C ÷ C/s = s

So, the unit of RC = s = second

So, the unit of the time constant RC is the second

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: