A charge of #24 C# passes through a circuit every #9 s#. If the circuit can generate #6 W# of power, what is the circuit's resistance?

2 Answers
May 30, 2017

Resistance is defined as the ability of the conductor to obstruct the flow of electric current through it. Resistance is basically defined by Ohm's Law as:-
#V=IR#

Explanation:

In the given question, we have:-
Charge = #24C = Q#
Time = #9s = t#

Rate of flow of current thorugh a cross-section of a conductor is givem by the following relation:-

#Q = It# where,
Q = Given charge
I = Current that flows
t = time (in second)

So, putting above stated values in this relation, we get:-

#24 = I . 9#
or # I = 24 / 9 A#

Power is defined as the ability to do work. Power is given by the formula:-

# P = VI# where,
P = Power in watt
V = Potential difference across the circuit
I = Current through the circuit

Putting values in the relation, we get:-

# 6 = V . 24/9 #
or # V = 6*9/24# V

As stated above, the expression for Ohm's Law gives resistance as:-
# R = V/I #

Hence, using the values obtained for V and I , we get:-

# R = 6 X 9/ 24 * 9/24 #
or # R = 0.84 Ω #

Hence, the resistance of the circuit is #0.84 Ω#.

May 30, 2017

The answer is #=843.75mOmega#

Explanation:

We apply the equation

#Q=It#

The charge is #Q=24C#

The time is #t=9s#

The current is #I=Q/t=24/9=8/3A#

The power

#P=UI#

But according to Ohm's Law

#U=RI#

So,

#P=RI*I=RI^2#

So,

the resistance is #R=P/I^2#

#=6/(8/3)^2=0.84375Omega#