2001 - JAMB Physics Past Questions and Answers - page 5

I =	_E
R+r

For parallel of 5Ω and 10Ω
¹/_R = ¹/₁₀ + ¹/₅ = ¹⁺²/₁₀ = ³/₁₀
∴R = ¹⁰/₃
Total R = 3¹/₃ + 3 x 1 = 7¹/₂
∴I = 6/7¹/₃ = ⁶/₁ x ³/₂₂ = ¹⁸/₂₂ = ⁹/₁₁
∴I = ⁹/₁₁

Here's how to solve this problem: 1. **Understand the Relationship:** When capacitors are connected in series to a DC source, they have the same charge (Q = CV, where C is capacitance and V is voltage). 2. **Energy Stored Formula:** The energy (U) stored in a capacitor is given by U = Q²/2C. 3. **Capacitors in series:** Because the capacitors are connected to the same voltage source, the voltage across each capacitor is the same. 4. **Calculate the Ratio:** * Let's denote the energy stored in capacitor P as Up and in Q as Uq. * Up / Uq = (Q²/2Cp) / (Q²/2Cq) = Cq

Here's how to solve this problem: 1. **Identify Series and Parallel Combinations:** C2 and C3 are in parallel, and the equivalent capacitance of this parallel combination is in series with C1. 2. **Calculate the equivalent capacitance of the parallel combination (C2 and C3):** C23 = C2 + C3 = 6 μF + 3 μF = 9 μF 3. **Calculate the equivalent capacitance of the entire circuit:** First we need to calculate the equivalent capacitance of the series combination of C1 and C23 1/C_eq = 1/C1 + 1/C23 1/C_eq = 1/2 + 1/9

0.0 E since one of the electric fields points in the opposite direction (left)

for a parallel R and X, when R = 5Ω,

effective resistance R =	5X
5+X

and when R = 2Ω

effetive resistance R =	2X
2+X

Thus since E = I(R+r), and if r = 0 then E = IR
∴(i) E = 3(5X/(5+x)); (ii) E = 6(2X(2+x))
∴3(5X/(5+X)) = 6(2X/(2+X))
=> (5X/(5+X)) = 2(2x/(2+X))
∴ (5X/(5+X)) = (4X/(2+X))
5x(2+x) = 4x(5+x)
10x + 5x² = 20x + 4x²
5x² - 4x² = 20x - 10x
=>x² = 10x
∴x² - 10x = 0
x(x - 10) = 0
∴ x = 0 or 10
∴ x = 10Ω

I_r.m.s = ^V_r.m.s/_Z
But Z =
√ R² + X_L² 

=
√ 4² + 3² 

=
√ 16 + 9 

=
√ 25 

∴I_r.m.s = ²⁴⁰/₅
= 48.0A

in vibrations in string, the fundamental frequency happens to be the first harmonic, and is given as

f₀ = V/2l.

Where V = Velocity of the sound wave, I = Length of the string.

The second harmonic is the first overtone given by

f₁ = V/l = 2f₀ ;

and the third harmonic happens to be the second overtone, given by

f₂ = 3V/2l = 2f₀.

Thus if V = 120m/s and l = 1.5m
Thus f₁ = 2f₀ = 2 x 40 = 80Hz
Thus f₂ = 3f₀ = 3 x 40 = 120Hz
Thus we have in order, 40Hz, 80Hz, 120Hz

Electrical Energy = IVt
= 4 x 240 x (1 x 60)
= 57600J
= 5.76 x 10⁴J

The angle of dip dip is the angle which the resultant earth's magnetic field makes with the horizontal.
At the magnetic equator, which is entirely along the horizontal this angle is zero