Electricity Numerical Quiz (Graded)

Instructions: Solve the problems below. Enter the numeric value (units are optional). Click Submit to see your score and the solutions.

1. A current of $0.5 \text{ A}$ is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit.

Coulombs

Answer: 300 C
Using $Q = It$, where $t = 10 \text{ min} = 600 \text{ s}$.
$Q = 0.5 \text{ A} \times 600 \text{ s} = 300 \text{ C}$ .

2. How much work is done in moving a charge of $2 \text{ C}$ across two points having a potential difference of $12 \text{ V}$?

Joules

Answer: 24 J
Work done $W = VQ$.
$W = 12 \text{ V} \times 2 \text{ C} = 24 \text{ J}$ .

3. How much current will an electric bulb draw from a $220 \text{ V}$ source if the resistance of the bulb filament is $1200 \, \Omega$?

Amperes

Answer: 0.18 A
By Ohm's Law $I = V/R$.
$I = 220/1200 = 0.18 \text{ A}$ .

4. An electric heater draws $4 \text{ A}$ at $60 \text{ V}$. What current will it draw if the potential difference is increased to $120 \text{ V}$?

Amperes

Answer: 8 A
Resistance $R = V/I = 60/4 = 15 \, \Omega$.
New Current $I_{new} = V_{new}/R = 120/15 = 8 \text{ A}$ .

5. A metal wire of length $1 \text{ m}$ and diameter $0.3 \text{ mm}$ has a resistance of $26 \, \Omega$ at $20^\circ\text{C}$. Calculate the resistivity.
(Enter your answer as the value $X$ in the format $X \times 10^{-6} \, \Omega \text{ m}$)

x 10^-6 Ω m

Answer: 1.84
$\rho = (RA)/l$ where $A = \pi(d/2)^2$.
Calculation yields $\rho = 1.84 \times 10^{-6} \, \Omega \text{ m}$ .

6. An electric lamp of resistance $20 \, \Omega$ and a conductor of $4 \, \Omega$ resistance are connected in series. Calculate the total resistance.

Ohms

Answer: 24 Ω
In series, $R_s = R_1 + R_2$.
$R_s = 20 + 4 = 24 \, \Omega$ .

7. Three resistors of $5 \, \Omega$, $10 \, \Omega$, and $30 \, \Omega$ are connected in parallel. What is the equivalent resistance?

Ohms

Answer: 3 Ω
$1/R_p = 1/5 + 1/10 + 1/30 = 10/30$.
Therefore, $R_p = 30/10 = 3 \, \Omega$ .

8. $100 \text{ J}$ of heat is produced each second in a $4 \, \Omega$ resistor. Find the potential difference across the resistor.

Volts

Answer: 20 V
$H = I^2Rt$. With $t=1$, $100 = I^2(4)$. So $I=5\text{ A}$.
$V = IR = 5 \times 4 = 20 \text{ V}$ .

9. An electric bulb is connected to a $220 \text{ V}$ generator. The current is $0.50 \text{ A}$. What is the power of the bulb?

Watts

Answer: 110 W
Power $P = VI$.
$P = 220 \times 0.50 = 110 \text{ W}$ .

10. A 400 W refrigerator runs 8 hours/day. Calculate the cost for 30 days at Rs 3.00 per kWh.

Answer: 288
Energy $= 400 \text{ W} \times 8 \text{ h} \times 30 = 96000 \text{ Wh} = 96 \text{ kWh}$.
Cost $= 96 \times 3.00 = 288 \text{ Rs}$ .

Electricity: Numerical Assessment