Question

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?

Answer 1

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`.

Answer 2

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`