###### Electric Field

What force will a charge of 1C feel when it is in the electric field with a strength of 100 V/m?

Input the correct answer in N.

$$F = EQ = 1\times 100= 100N$$, where E is the strength of the electric field and Q is the charge of a particle.

###### Potential

How much kinetic energy will a particle with a charge of 10 mC gain while accelerating throgh a potential difference of 1kV?

$$E_k = VQ = 1000\times 0.01 =10J,$$ where V is the accelerating potential difference, Q is a charge of the particle.

###### Electric Field Strength between two planes

Two planes are placed parallel in a vacuum; there is a potential difference of 10kV between them. The distance between the planes is 10cm. Calculate the electrical field strength between these two planes

$$E = V/d = 1000/0.1 = 10000V/m,$$ where V is a potential difference between the planes and d is the distance between the planes.

###### Coulomb's force

Calculate the force between two charged particles with charges of Q1 = 1mC and Q2 = 2mC placed at the distnace of 2m in vacuum.

$$F_{coulomb}={kQ_qQ_2\over r^2}\approx {8.99\times10^9\times 0.001\times0.002\over4}=4495N$$

###### Capacitor

What is the capacitance of a capacitor which can store 24mC of charge when the potential difference across it is 12V?

$$C = Q/V =24\times 10^{-3}/12 = 2mF$$

###### Energy stored on capacitor

What is the energy stored on a 400 $$\mu F$$ capacitor which has 2mC of charge on it?

$$E = {Q^2\over 2C} ={(2\times10^{-3})^2\over2 \times 400\times10^{-6}} = 0.005J$$

###### Time constant

Select the correct expression for time constant of RC-circuit.

$$\tau = RC$$. Time constant shows how long it takes for a resistor-capacitor system to discharge.

###### Discharge of capacitor

А 0.04 F capacitor is fully charged by a 5V supply and is then connected to discharge through a $$800\Omega$$ resistor. How much charge remains on the capacitor after 20 seconds?

Intial charge of the capacitor is $$Q_0=CV=0.2C$$.

The function describing remaining charge is $$Q(t)=Q_0e^{-t/RC}=0.2\times e^{-20/{800\times0.04}}\approx0.11C$$.

###### RC

А 0.02 F capacitor is fully charged by a 5 V supply and is then connected to discharge through a $$800\Omega$$ resistor. What is the potential difference on the capacitor after 10 seconds?

$$V =V_0\times e^{-t/RC} = 5\times e^{-10/800\times 0.02}\approx2.68V$$

###### Discharge current

А 0.02 F capacitor is fully charged by a 5 V supply and is then connected to discharge through a $$800\Omega$$ resistor. What is the discharge current after 10 seconds?

Initial current is $$I_0 =V_0/R= 5/800=6.25mA$$.
$$I = I_0\times e^{-t/RC}=6.25\times e^{-10/0.02\times 800}\approx3.35mA$$